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.

3478. To some there was also represented the tabernacle with the ark, for to those who, when they lived in the world, have taken very great delight in the Word such things are presented to them visually. So on the occasion referred to they saw the tabernacle with all its furnishings; that is to say, they saw its courts, its curtains round about, its veils inside, the golden altar or altar of incense, the table where the loaves were placed, the lampstand, and the mercy-seat with the cherubim. At the same time these upright spirits were allowed to perceive what each particular thing meant. It was the three heavens that were represented by the tabernacle, and the Lord Himself by the testimony inside the ark, above which there was the mercy-seat. And to the extent their sight was opened they saw within those objects more heavenly and Divine things, of which they had had no knowledge at all during their lifetime. And what was amazing, every least thing there, even every hook or ring, was representative. Consider merely the bread placed on the table. Within this as within a representative and symbol they perceived the food on which angels live, and so perceived celestial and spiritual love together with all the bliss and happiness that the angels enjoy. And within that love, also that bliss and happiness, they perceived the Lord Himself as the bread or manna from heaven. They perceived more besides from the shape, position, and number of the loaves, and from the gold which was around them, and from the lampstand which lit up those things and displayed further representations of things that are indescribable. The same was so with everything else in the tabernacle. From all this one might also see that the religious observances or the representatives of the Jewish Church contained all the arcana of the Christian Church, and also that those to whom the representatives and meaningful signs of the Old Testament Word are disclosed are able, while living in the world, to know and perceive the arcana which belong to the Lord's Church on earth. And when they enter the next life they are able to know and perceive the arcana of arcana which belong to the Lord's kingdom in heaven.