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.

553. In heaven those who are moved by mutual love are constantly approaching the spring-time of their youth. And the more thousands of years they live the more joyful and happy the spring-time which they are approaching. This process continues for ever, constantly bringing increases in joy and happiness in proportion to the advance and upward progress in mutual love, charity, and faith. Those of the feminine sex who have died worn out with age but who had lived in faith in the Lord, in charity towards the neighbour, and in happy conjugial love with their husbands, as the years pass by come more and more into the first freshness of youth and early womanhood, and into a beauty that excels every idea of beauty which the eye can possibly behold. In fact it is goodness and charity forming and producing a likeness of itself, and causing the joy and beauty of charity to shine out of every individual feature of the face in such a way that these too are forms of charity. When some people have seen these they have been dumbfounded.

[2] The form which charity takes is so plainly visible in the next life that charity itself is that which produces the form, as well as being that which is portrayed within it. Indeed that form is such that the whole of an angel, especially the face, is so to speak charity - charity which is visible to the eye and perceptible to the mind. When it is beheld that form is one of indescribable beauty which stirs with charity the inmost life itself of the beholder's mind. Through the beauty of that form truths of faith are displayed in a visual image from which they also are perceived. People who have lived in faith in the Lord, that is, faith that inheres in charity, in the next life become such forms, that is, forms of beauty. All angels are such forms, endlessly varying; and it is these forms that constitute heaven.