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.

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