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 #1806
1806. That 'He brought him outside' means the sight possessed by the Interior Man, which from external things sees internal things, becomes clear from the meaning of 'bringing outside' and at the same time from what follows next. Internal things are 'brought out' when someone looks with his physical eyes at the starry sky and from this thinks about the Lord's kingdom. Whenever a person sees anything with his eyes, yet so to speak does not see the things he sees, but from them sees or thinks of the things that belong to the Church or to heaven, his interior sight, that is, the sight of his spirit or soul, is being 'brought outside'. Strictly speaking the eye itself is nothing else than the sight of the spirit itself 'brought outside', the specific purpose of this being that from external things a person may see internal things, that is, that from objects existing in the world he may reflect continually on things that exist in the next life, for it is for the sake of that life that he lives in the world. Such was the sight of the Most Ancient Church; such is the sight of angels who reside with man; and such was the Lord's sight.
(References: Genesis 15:5)