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.

212. That 'the eyes becoming opened' means a dictate coming from within is clear from similar usages in the Word, such as that which Balaam adopts when speaking about himself. Because he had visions he calls himself' a man who has had his eyes opened', Numbers 24:3-4. And in the case of Jonathan when on tasting from the honeycomb he experienced a dictate from within indicating that doing so was evil, it is said that his eyes saw, that is, they were enlightened for him to see the thing he had not known up to then, 1 Samuel 14:27, 29. Also, many times in the Word, the eyes stand for the understanding, and so for an inner dictate from the understanding, as in David,

Lighten my eyes, lest I sleep [the sleep of] death. Psalms 13:3.

'Eyes' here stands for the understanding. In Ezekiel,

They have eyes to see but they see not. Ezekiel 11:2.

Here they stand for those who do not wish to understand. In Isaiah,

Plaster over their eyes, lest they see with their eyes. Isaiah 6:10.

This stands for their being blinded to prevent their understanding. Through Moses the people were told,

Jehovah has not given you a heart to know, and eyes to see, and ears to hear. Deuteronomy 29:4.

'Heart' stands for the will, and 'eyes' for the understanding. It is said of the Lord in Isaiah 42:7 that He will open eyes that are blind; and in the same prophet,

Out of thick darkness and out of darkness the eyes of the blind will see. Isaiah 29:18.