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.

3379. 'And I will give to your seed all these lands' means derivative Churches. This is clear from the meaning of 'seed' as truths, and so those who possess truths and are consequently called 'the sons of the kingdom', dealt with above in 3373, and from the meaning of 'lands' as rational concepts which, when enlightened from the Divine, are appearances of truth, also dealt with above, in 3368, and so those with rational concepts enlightened from the Divine, or what amounts to the same, those who dwell in heavenly light. Since none but those who are in the Lord's kingdom in the heavens, that is, in heaven, and those who are in the Lord's kingdom on earth, that is, in Churches, dwell in that heavenly light, it is evident that 'these lands' means Churches. For Churches are not Churches on account of their being called such and of their confessing the Lord's name, but on account of the good and truth of faith that exist in them. Good and truth of faith themselves are what make a Church, indeed they are the Church, for present within the good and truth of faith there is the Lord, and where the Lord is, there is the Church also.