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.

2701. 'God opened her eyes' means intelligence. This is clear from the meaning of 'opening' - and that it is God who did so - and also from [the meaning] of 'the eyes', as conferring intelligence; for 'the eyes' means the understanding, see 212, as also does 'sight' or 'seeing', 2150, 2325. The expression 'God opens the eyes' is used when He opens interior sight or the understanding, which opening is accomplished by means of an influx into the rational part of the person's mind, or rather into the spiritual part of his rational. The route taken by this influx is the soul, that is, the internal route, of which the person himself is not aware. This influx is his state of enlightenment in which the truths he hears or reads about are confirmed for him by a kind of perception existing within, in the understanding part of his mind. The person himself believes that this enlightenment is innate within himself and that it springs from his own power of understanding; but in this he is very much mistaken. This enlightenment consists in an influx from the Lord by way of heaven into that person's dim, mistaken, and specious sight of things, and by means of the good there causes the things which he believes to become imitations of truth. Only those who are spiritual however are blessed with enlightenment in spiritual matters of faith; and this is the meaning of the expression 'God opens the eyes'.

[2] The reason why 'the eye' means the understanding is that the sight belonging to the body corresponds to that belonging to its spirit, which is the understanding. And because it has this correspondence 'the eye' in the Word, in almost every place where it is mentioned, means the understanding, even where people believe something other is meant, as where the Lord says in Matthew,

The lamp of the body is the eye. If the eye is sound, the whole body is full of light. If the eye has been evil the whole body has been made full of darkness. If therefore the light is darkness, how great is the darkness! Matthew 6:22-23; Luke 11:34.

Here 'the eye' is the understanding, the spiritual constituent of which is faith, as also is shown by the explanation added here - 'if therefore the light is darkness, how great is the darkness!' Similarly in the same gospel,

If your right eye causes you to stumble, pluck it out and throw it away from you. Matthew 5:29; 18:9.

'The left eye' is the understanding part of the mind, whereas 'the right eye' is its affection. The command to pluck out the right eye means that if it causes one to stumble one's affection must be disciplined.

[3] In the same gospel,

Blessed are your eyes, for they see, and your ears, for they hear. Matthew 13:16.

And in Luke, Jesus said to the disciples, Blessed are the eyes which see what you see. Luke 10:23.

Here 'the eyes which see' means intelligence and faith, for it was not the mere fact that they saw the Lord and also His miracles and works that caused any one of the disciples to be blessed but the fact that they could grasp things with their understandings and had faith, meant by 'seeing with the eyes', and that they were obedient, meant by 'hearing with the ears'. As regards 'seeing with the eyes' meaning to see with the understanding and also to have faith, see 897, 2325. For the understanding is the spiritual complement of sight, and faith the spiritual complement of the understanding. The sight of the eye is received from the light of the world, the sight of the understanding from the light of heaven flowing into things which belong to the light of the world; but the sight of faith is received from the light of heaven. This is the origin of such phrases as seeing with the understanding and seeing with faith. 'Hearing with the ear' means being obedient, see 2542.

[4] In Mark,

Jesus said to the disciples, Do you not yet know nor understand? Do you still have your heart hardened? Having eyes do you not see, and having ears do you not hear? Mark 8:17-18.

Here it is evident that 'having eyes but not seeing' means not wishing to understand and not believing. In Luke,

Jesus said of the city, Would that you knew the things that make for your peace! But such is hidden from your eyes. Luke 19:41-42.

And in Mark,

By the Lord has this been done, and it is marvellous in our eyes. Mark 12:11.

Here 'hidden from the eyes' and 'marvellous in the eyes' mean to be so to the understanding, as is well known to everyone from the meaning of 'the eyes' even in everyday speech.