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.

214. "'And to anoint your eyes with eye salve, that you may see.'" This symbolically means, so as to heal their understanding, to keep them from profaning and falsifying genuine truths of wisdom.

Eyes symbolize the intellect, and the sight of the eyes intelligence and wisdom, as may be seen in no. 48. And since eye salve symbolizes medicine for it, it follows that to anoint the eyes with eye salve means, symbolically, to heal the intellect, so that it may see truths and become wise. Otherwise the genuine truths of the Word are profaned and adulterated.