We should probably understand it this way. In this life we do not “see” because our inherent sinfulness keeps us from seeing him. Sin always separates us from the Lord. In this context, “seeing God” means to have a deep experience of God, to know him intimately and personally.  All successful marriages discover this truth on a human level.  The longer you live with another person, the more you get to know them as they really are.  Transparency begets intimacy.  In a good marriage, there is nothing hidden because there is nothing to hide. but no two people truly “see” each other in the deepest sense. Even after 36 years, there is much about my wife I am still learning.

Let me summarize this beatitude in a two short statements:

1.  In this life a pure heart means a deep walk with God.
2.  In eternity a pure heart means a new experience of God.

This is what Psalm 24 means when it asks “Who may ascend the hill of the Lord? Who may stand in his holy place?”  The answer is simple:  “He who has clean hands and a pure heart.”  He will receive a blessing from the Lord.  He will be vindicated by God himself.

In eternity we will see as much of God as it is possible for us to see. And we will never come to the end of who God is.

See The Tragedy of Double Vision.