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.

1584. That 'Lot lifted up his eyes' means that the external man received light from the internal is clear from the meaning of 'lifting up the eyes', which is seeing, in the internal sense, perceiving. Here 'lifting up the eyes' means receiving light, for this expression is used in reference to Lot, or the external man; and by perceiving the nature of the External Man when joined to the Internal Man, that is, the nature of its beauty, the external man receives light from the internal and possesses the Divine vision that is the subject here. Nor can there be any doubt that when He was a boy, the Lord as regards His external Man frequently had such Divine vision, for He alone was to join the external Man to the internal Man. The External Man was His Human Essence, while the Internal Man was His Divine Essence.