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.

637. The implications of 'I will destroy them together with the earth' meaning that the human race would perish together with the Church are as follows: If the Lord's Church had been completely wiped out on earth, the human race could not have remained in being at all, for all without exception would have perished. As previously stated, the Church is as the heart. As long as the heart is alive, surrounding organs and limbs are able to live as well. But the moment the heart dies, everything else dies as well. The Lord's Church on earth is as the heart, and from it the human race, even that part of it lying outside of the Church, has life. The reason why is totally unknown to anybody. But so that something of this may be known, let it be said that the whole human race on earth is like the body and all its parts, with the Church resembling the heart. And if there were no Church, with which as a kind of heart the Lord might unite Himself by way of heaven and the world of spirits, there would be a severance; and once the human race was severed from the Lord it would perish instantly. This is the reason why since man was first created there has always been some Church in existence; and as often as the Church has begun to perish it has nevertheless remained with certain people.

[2] This was also the reason why the Lord came into the world. Unless, in His Divine mercy, He had come, the whole human race on this planet would have perished, for at that time the Church was nearing its end, and scarcely any good or truth was surviving. The reason the human race cannot possibly live unless it is joined to the Lord by way of heaven and the world of spirits is that regarded in himself man is even lower than animals. Left to himself he would rush to ruin himself and everybody else, for he has no other desire than to destroy himself and everybody else. His order ought to be as one person loving another as he does himself, but at present everyone loves himself more than others and so hates everybody else. Dumb animals are quite different however, for theirs is an order which they do live according to; and so they live wholly according to the order that is theirs, whereas man lives altogether contrary to order. Consequently unless the Lord had taken pity on man and by means of angels joined him to Himself he could not possibly live for a single moment. Of this man has no knowledge.