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 #8792
8792. 'Jehovah will come down before the eyes of all the people' means, the coming of the Lord will occur, and enlightenment at that time. This is clear from the meaning of 'coming down', when said of Jehovah, that is, the Lord, as His presence through influx, thus His coming - the coming of the Lord being meant here by Jehovah's coming down before the eyes of all the people. Jehovah appeared in an outward form before those people because they could not perceive His presence in any other way; for they were inwardly devoid of the goodness and truth in which the Lord is present with others, 8787. Enlightenment at that time is meant by 'before the eyes of all the people', for 'the eye' in the internal sense is the understanding, and consequently the sight of the eye is the perception belonging to faith, which owes its existence to the light of heaven, so that 'before the eyes' is enlightenment. For the meaning of the eye as the understanding, and its sight as the perception belonging to faith, see 4403-4421, 4523-4534.
(References: Exodus 19:11)