Blessed are the pure in heart, for they will see God.
The word for pure in the Scriptures, like the word for light, is often connected with clean. It does not mean phyiscial cleanliness, but a heart that is like clear unblemished, polished, glass. It's a heart that is like glass so polished that its owner -- God-- can see Himself in it and nothing else. No smudge or blemish or human sin dirties such a heart.
Can a human heart make itself accurately reflect God's holiness, character, goodness, love, patience, justice, mercy, joy, peace, righteousness, and truth by its own strength? No. But realizing we cannot attain to the holiness of God without God helping us us the beginning of the honest and humility of a truly pure heart.