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.

5601. 'And we told him according to the tenor of his words' means its accordant discernment of these matters. This is clear from the meaning of 'telling' or 'pointing out' as discerning, dealt with in 3608, for in the spiritual world or heaven those there have no need to tell what they are thinking since all thoughts are communicated, 5597, which is why 'telling' in the spiritual sense means discerning; and from the meaning of 'according to the tenor of his words' as in an accordant manner, for they are matters that he wished to discern.