It’s common to say “I see” when we understand something. And indeed, “seeing” in the Bible represents grasping and understanding spiritual things. So it makes sense that the eyes, which allow us to see, represent the intellect, which allows us to understand spiritual things.
This can also be used in the negative, of course; the Bible speaks of people having eyes and refusing to see, and the Lord when He was in the world advised plucking out an offending eye. These represent a refusal to acknowledge truth, or being misled by falsity.
Arcana Coelestia #3863
3863. 'For she said, Because Jehovah has seen' in the highest sense means foresight, in the internal sense faith, in the interior sense understanding, and in the external sense sight - faith received from the Lord being meant here. This is clear from the meaning of 'seeing', dealt with below. What has been presented above shows that the twelve tribes, named after the twelve sons of Jacob, meant all things forming part of truth and good, or of faith and love, and so all aspects of the Church. It also shows that each tribe meant some universal division, and so the twelve tribes the twelve universal divisions which embrace and include within themselves every specific thing which is part of the Church, and in the universal sense everything that is part of the Lord's kingdom. The universal division meant by 'Reuben' is faith. The reason faith is the first universal division is that when a person is being regenerated, or becoming the Church, he must first learn and absorb aspects of faith, that is, of spiritual truth, for it is by means of doctrine about faith or truth that he is led into regeneration. For man is such that of himself he does not know what heavenly good is but has to learn about it from doctrine, which is called the doctrine of faith. Every doctrine of faith has life as the end in view, and because it has life it also has good in view, for good is the sum and substance of life.
 Controversy existed among the ancients over which was the firstborn of the Church, whether it was the truth of faith or whether it was the good of love. Those who said that the truth of faith was the firstborn based their conclusions on the outward appearance and decided that such truth was the firstborn because it is and must be learned first and because a person is led by means of it into good. But they did not know that good is essentially the firstborn and that it is instilled by the Lord through the internal man so that he may adopt and accept the truth which is brought in by way of the external. They did not know that good holds life from the Lord within it, or that truth does not possess any life except that which comes through good, so that good is the soul of truth by making truth its own and clothing itself with it as the soul does the body. From this it may be seen that to outward appearance truth occupies first place and is so to speak the firstborn while a person is being regenerated, though essentially good occupies first place and is the firstborn, and does actually come to occupy it once he has been regenerated. For the truth of this, see 3539, 3548, 3556, 3563, 3570, 3576, 3603, 3701.
 The subject in this and previous chapters being the regeneration of the natural - at this point its first state, which is a state of being led by means of truth into good - the first son of Jacob, who was Reuben, was so named from the phrase Jehovah seeing, which in the internal sense means faith originating in the Lord. Regarded in itself faith consists in faith in the understanding and faith in the will. Knowledge and understanding of the truth of faith is called faith in the understanding, but willing the truth of faith is called faith in the will. The former - faith in the understanding - is the faith meant by 'Reuben', but the latter - faith in the will - is that meant by 'Simeon'. It may be seen by anyone that faith existing in the understanding, or the ability to understand truth, comes before faith existing in the will, or the actual willing of it. For when a person does not know of something, such as heavenly good, he must first come to know of its existence and then to understand what it is before he is able to will it.
 'Seeing' in the external sense means sight, as is clear without explanation. 'Seeing' in the interior sense means the understanding, as is likewise clear, for the sight that the internal man has is nothing else than the understanding, which also is why in everyday speech the understanding is called internal sight, and the word light is used in reference to it as well as to external sight and is called the light of the understanding. 'Seeing' in the internal sense means faith received from the Lord, as is clear from the consideration that interior understanding has no other objects than those of truth and good, for these are the objects of faith. This interior understanding, or internal sight, which has truths of faith as its objects, does not show itself so plainly as the understanding does which has truths to do with public and private life as its objects, the reason being that it exists inside this latter understanding and dwells in the light of heaven, which light is in obscurity as long as a person dwells in the light of the world. Nevertheless it does reveal itself with those who are regenerate, in particular by means of conscience. 'Seeing' in the highest sense clearly means foresight, for the intelligence spoken of in reference to the Lord is an infinite intelligence, which is nothing else than foresight.
 That 'seeing' after which Reuben was named means in the internal sense faith received from the Lord is evident from very many places in the Word, of which let the following be brought forward: In Moses,
Jehovah said to Moses, Make a serpent and set it on a standard, and it will be that everyone who has been bitten, when he sees it, will live. And Moses made a serpent of bronze and set it on a standard. And so it was, if a serpent had bitten a man, when he looked at the serpent of bronze, that he was restored to life again. Numbers 21:8-9.
'The bronze serpent' represented the Lord's external sensory perception, which is natural, see 197 - 'bronze' meaning that which is natural, 425, 1551. Faith in Him was represented by the restoration to life again of those who saw it, that is, looked at it, as the Lord Himself teaches in John,
As Moses lifted up the serpent in the wilderness, so must the Son of Man be lifted up, that everyone who believes in Him may not perish but have eternal life. John 3:14-15.
 In Isaiah,
The Lord said, Go and say to this people, Hearing, hear - but do not understand; and seeing, see - but do not comprehend. Make the heart of this people fat and their ears heavy, and plaster over their eyes, lest they see with their eyes and hear with their ears, and their heart understands. Isaiah 6:9-10.
Here it is quite evident that 'seeing, see - but do not comprehend' means understanding what is true and yet not acknowledging. The words 'plastering over their eyes, lest they see with their eyes' means depriving them of the understanding of truth, faith in the Lord being meant in this case by 'seeing', as is clear from the Lord's words in Matthew 13:13-14, and in John 12:36-37, 39-40.
 In Ezekiel,
Son of man, you are dwelling in the midst of a rebellious house, who have eyes to see but they do not see, who have ears to hear but they do not hear. Ezekiel 12:2
'Eyes to see but they do not see' stands for their being able to understand the truths of faith but not willing them. They do not will them on account of evils, meant by 'a rebellious house', which bring an untrue light to falsities and darkness to truths, in accordance with the following in Isaiah,
They were a rebellious people, lying sons, sons who did not wish to hear the law of Jehovah, who said to the seers, Do not see; and to those who had visions, Do not see for us things that are right, tell us smooth things, see illusions. Isaiah 30:9-10.
This people walking in darkness have seen a great light; those dwelling in the land of the shadow of death, upon them has the light shone out. Isaiah 9:2.
'Seeing a great light' stands for receiving and believing the truths of faith. It is over those who have faith that heavenly 'light' is said 'to shine out', for the light which is shed in heaven is Divine Truth coming from Divine Good.
 In the same prophet,
Jehovah has poured out over you a spirit of slumber, and has closed your eyes, the prophets and your heads, the seers, He has covered. Isaiah 29:10.
'Closing the eyes' stands for closing the understanding of truth - 'the eye' meaning the understanding, see 2701. 'Covering the seers' stands for covering those who know and teach the truths of faith. 'Seers' in former times were called prophets, and prophets mean those who teach as well as meaning the truths of doctrine, see 2534. In the same prophet,
The priest and the prophet err through strong drink, they err among those who see, they are tottery in judgement. Isaiah 28:7.
Here the meaning is similar. 'The judgement in which they are tottery' means the truth of faith, see 2235. In the same prophet,
The eyes of those who see will not be closed, and the ears of those who hear will listen. Isaiah 32:3.
Here the meaning is similar.
 In the same prophet,
Your eyes will behold the king in his beauty, they will see a land stretching far. Isaiah 33:17.
'Beholding the king in his beauty' stands for beholding truths of faith which come from the Lord and are called beautiful by virtue of good. 'Seeing a land stretching far' stands for seeing the good of love. For 'the king' means the truth of faith, see 1672, 2015, 2069, 3009, 3670, this being called beautiful by virtue of good, 553, 3080, 3821; and 'a land' means the good of love, 620, 636, 3368, 3379. In Matthew,
Blessed are the pure in heart, for these will see God. Matthew 5:8.
Here it is quite evident that 'seeing God' means believing in Him, and so seeing Him by faith, for people who possess faith, from faith see God, since God is within faith and is that within faith which constitutes true faith.
 In the same gospel,
If your eye causes you to stumble pluck it out. It is better for you to enter into life one-eyed than having two eyes to be thrown into the Gehenna of fire. Matthew 18:9.
Here, as is quite evident, 'the eye' does not mean the eye. Nor does it mean that the eye has to be plucked out, for it is not the eye that causes the stumbling but the understanding of truth meant here by 'the eye', 2701. The law that it is better not to know and grasp the truths of faith than to know and grasp them and yet to lead a life of evil is what is meant by 'better to enter into life one-eyed than having two eyes to be thrown into the Gehenna of fire'.
 In the same gospel,
Blessed are your eyes, for they see, and your ears, for they hear. Truly, I say to you, many prophets and righteous men desired to see what you see, but did not see. Matthew 13:13-17; John 12:40.
'Seeing' stands for knowing and understanding the things that constitute faith in the Lord, and so stands for faith. For it was not their seeing the Lord and seeing His miracles that made them 'blessed' but their believing, as becomes clear from the following words in John,
I said to you that you have both seen Me and not believed. This is the will of Him who sent Me, that everyone who sees the Son and believes in Him may have eternal life. No one has seen the Father except Him who is with the Father; He has seen the Father. Truly, truly, I say to you, He who believes in Me has eternal life. John 6:36, 40, 46-47.
'Seeing and not believing' stands for knowing the truths of faith and not accepting them, 'seeing and believing' for knowing them and accepting them. The words 'No one has seen the Father except Him who is with the Father' stands for not being able to acknowledge Divine Good except through Divine Truth - 'the Father' being Divine Good and 'the Son' Divine Truth, see 3704. Consequently the internal sense is that nobody is able to possess heavenly good unless he acknowledges the Lord.
(References: Matthew 13:16-17)
 Similarly in the same gospel,
Nobody has ever seen God; the only begotten Son who is in the bosom of the Father, He has made Him known. John 1:18.
And in the same gospel,
Jesus said, He who sees Me sees Him who sent Me. I have come as Light into the world in order that everyone who believes in Me may not remain in darkness. John 12:45-46.
Here it is explicitly stated that 'seeing' means believing or possessing faith. And in the same gospel,
Jesus said, If you know Me you know My Father also. And from now you know Him and have seen Him. He who has seen Me has seen the Father. John 14:7, 9.
In the same gospel,
The Spirit of truth the world cannot receive because it neither sees Him nor knows Him. I will not leave you orphans, I am coming to you. Yet a little while, the world will see Me no longer, but you will see Me; because I live you will live also. John 14:17-19.
'Seeing' stands for possessing faith, for it is solely through faith that the Lord is seen. Actually faith is the eye of love, since it is from love through faith that the Lord is seen, love being the life of faith. Hence His statement, 'You will see Me; because I live you will live also'.
 In the same gospel,
Jesus said, For judgement I came into this world, that those who do not see may see, but that those who see may become blind. The Pharisees said, Are we also blind? Jesus said to them, If you were blind you would have no sin; but now you say, 'We see', therefore your sin remains. John 9:39-41.
'Those who see' stands for those who imagine themselves to be more intelligent than everybody else. Of them it is said that they will become blind, that is, will not acquire faith. 'Not seeing' or being blind is used in reference to those immersed in falsities, and also to those who have no knowledge [of the truth], see 2383. In Luke,
To you it has been given to know the mysteries of the kingdom of God, but for everyone else in parables, that seeing they may not see, and hearing they may not hear. Luke 8:10.
Here the meaning is similar. In the same gospel,
I tell you truly, There are some of those standing here who will not taste death until they see the kingdom of God. Luke 9:27; Mark 9:1.
'Seeing the kingdom of God' stands for believing. In the same gospel,
Jesus said to the disciples, The days will come when you will desire to see one of the days of the Son of Man, but you will not see. Luke 17:22.
This refers to the close of the age or last period of the Church when no faith exists any longer.
 In the same gospel,
It happened, when Jesus was at table with them, that He took the bread and said a blessing, and broke it and gave to them. Then their eyes were opened and they recognized Him. Luke 24:30-31.
The meaning of this event was that the Lord comes into sight through good, but not through truth devoid of good; for 'bread' means the good of love, 276, 680, 2165, 2177, 3478, 3735, 3813. From these and many other places it is clear that 'seeing' in the internal sense means faith received from the Lord, for no other faith exists which is truly faith except faith which comes from the Lord. This is also the faith that enables a person to see, that is, to believe. But faith originating in self or a person's proprium is not truly faith, for it causes him to see falsities as truths and truths as falsities; or if he does see truths as truths he does not truly see them because he does not believe them. For in them he sees himself and not the Lord.
 That 'seeing' means possessing faith in the Lord is quite evident from what has been stated often about the light of heaven, namely that because it flows from the Lord the light of heaven holds intelligence and wisdom within it, and so holds faith in Him since faith in the Lord is inwardly present in intelligence and wisdom. Consequently seeing by that light, as angels do, can mean nothing else than faith in the Lord. The Lord Himself too is within that light because it proceeds from Him. That light is also the light which shines within the conscience of those who possess faith in Him, though no one is directly conscious of its doing so as long as he lives in the body, for during that time the light of the world is obscuring that light.
(References: Genesis 29:32)