The heart – no big surprise – represents love, what we care about most. To be pure – again no big surprise – represents being devoid of evil. So the pure in heart are those who love what is good, with no shadow of evil.

The meaning of "seeing God" might be a little more surprising. "Seeing" has to do with understanding what is true, and "God" represents divine truth, or the first and most complete expression of the Lord's infinite love. So this is really more an intellectual thing than an emotional one; the verse is saying that those who have love in their hearts will be able to understand what the Lord wants from us, will be given the knowledge and wisdom to put their love into action.

(Odkazy: Arcana Coelestia 3863 [9]; The Doctrine of the New Jerusalem Regarding the Sacred Scripture 57)

57. 3. Genuine truth, of which doctrine ought to consist, is apparent in the Word’s literal sense only to people who are enlightened by the Lord. Enlightenment comes from the Lord alone, and it is found in people who love truths because they are true and apply them to useful life endeavors. Enlightenment in the Word is not found in others.

Enlightenment comes from the Lord alone because the Lord is present everywhere in the Word. The reason enlightenment is found in people who love truths because they are true and apply them to useful life endeavors is that they are in the Lord and have the Lord in them. For the Lord embodies His Divine truth. When this truth is loved because it is Divine truth — and it is loved when it is applied to useful endeavor — then the Lord is present in the person in that truth.

This, too, the Lord teaches in John:

In that day you will know that...you (are) in Me, and I in you. He who has My commandments and keeps them, is he who loves Me.... ...and I will love him and manifest Myself to him...and (I) will come to him and make (My) home with him. (John 14:20-21, 23)

And in Matthew:

Blessed are the pure in heart, for they shall see God. (Matthew 5:8)

These are the people who are enlightened when they read the Word, and with whom the Word shines and is translucent.