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 #5810
5810. 'And I will set my eye on him' means a flowing in at this point of truth from good. This is clear from the meaning of 'setting one's eye on someone' as communicating the truth of faith. For 'the eye' corresponds to the sight of the understanding and to the truths of faith, see 4403-4421, 4523-4534; and since 'setting one's eye on someone means communication, a flowing in is meant too. Internal good, which 'Joseph' represents, does not communicate with the truth represented by 'Benjamin' except by means of a flowing in, because that truth is lower.
(References: Genesis 44:21)