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.

4410. Much experience has made it plain to me that the sight of the left eye corresponds to the truths seen by the understanding and the right eye to the affections for truth which are also present with the understanding; and therefore that the left eye corresponds to the truths of faith and the right eye to the goods of faith. The reason why such correspondence exists is that the light which comes from the Lord is heat as well as light, the light itself being the truth which proceeds from the Lord and the heat the good. This, together with influx into the two hemispheres of the brain, is the origin of that correspondence; for those who are governed by good are on the Lord's right, and those governed by truth on His left.