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.

10160. When asked whether on their planet they live subject to the rule of governors or of kings they replied that they do not know what such rule is and that they live subject only to themselves, divided into clans, families, and households. When asked further whether they are therefore free from anxiety they said that they are free from it since one family is not at all envious of another and has no wish at all to take anything away from it. They were annoyed by such questions, as though these charged them with the existence of enmity and the existence of some safeguard against robbers. What more, they declared, do people need to have apart from food and clothing, in order that they may dwell contented and at peace, subject only to themselves?

[2] It was recognized, they said, from the most ancient people who were from our own planet that these people had in their times led a similar kind of life and that then they had not known what it was to be stirred by self-love to rule over others or to be moved by love of the world to accumulate possessions in excess of the necessities of life. They perceived also that those people then enjoyed inward and at the same time outward peace, so that heaven dwelt with mankind. Those times were therefore referred to by the writers of old as the golden age, and were described as ones in which people were led to do what was right and fair by the law written on their hearts.

[3] The circumstances in which they lived in those times are described in the Word as ones in which they dwelt by themselves, in security, subject only to themselves, without doors or bars. Indeed they lived in tents, and therefore as a reminder of this a tent was made to serve as the house of God, and afterwards the feast of tents or tabernacles was established, when they were to rejoice heartily. And since those who led this kind of life were devoid of the insane love of ruling for selfish reasons and of gaining the world for worldly reasons, heaven came down among them, and the Lord was seen in the human form by many.