'The liver,' as in Exodus 29:13, signifies interior purification, and 'the caul above the liver,' the inferior good of the external or natural self.

(Odkazy: Arcana Coelestia 10031)

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.