This is a remarkable promise. Would you like to see God? Then first purify your heart.
Notice this is not just ritual purity, which had been the focus of the Law of Moses. Christ is replacing earlier ritual based purity with internal purity.
He speaks about the heart, rather than the hands and feet. Christ is speaking about beholding God, unlike the retreat Israel took from the offered opportunity at Sinai. (See D&C 84: 22-25.) He is returning to the time of Moses, when a higher way might have been chosen.
Purity of the heart is a borrowed benefit from the Savior. Man cannot become clean before God without the necessary offering of a sacrifice. The Law of Moses taught this, but Christ would actually bring it to pass. (See, e.g., Alma 34: 36.)
When we repent we turn to Christ and listen to and follow Him. Until then, we are not even facing the right direction in life.
Some reminders of how the heart may be purified:
-Let virtue constantly prevail in your thoughts. (D&C 121: 45.)
It is also interesting that what must be "pure" is the "heart." There are so many other things one might measure. But what the Lord looks upon to determine purity is the "heart."
I've said that there is almost nothing about us that can become perfect in this life. The only thing that can approach perfection, however, is our intent. We can mean to follow God at all times. Even if the dilemmas of life make it impossible to actually do so, we can still intend to follow Him. We may not even know if what we are doing pleases Him, or how to resolve conflicting interests or commandments. We may even be making a mistake, but if our intent is right, our hearts may be pure.
This is also one of the reasons we cannot judge another. They may be weak, foolish and error prone, but if they intend to be doing the right then God alone can measure their heart and decide whether they are approved. It would take a God to know if the person's life, training, understanding and intent are pure before Him. I suspect there are those we look upon as deluded and even evil but the Lord views them with compassion and understanding. He may find their hearts to be perfect even before the heart of the proud who claim they have and follow the truth. Though a person may misunderstand a great deal, still if they have love for their fellow man, relieve suffering where they can, give patience to the foolish and water to the thirsty, they may be perfect before God. (Luke 18: 9-14.)
There are so many illusions here. Some who are regarded as high and lifted up by God, temperate in their conduct, studying how they are seen by others before acting; are in fact wretched, miserable, poor and naked. (Rev. 3: 14-17.) I say with authority that there are some regarded as the very chiefest of the righteous among the Latter-day Saints who are before God wretched, miserable, poor and naked. They cannot survive even a glance from His all seeing eye. Yet they pretend they share in His vision, when they do not.
How few hearts are pure before God. How rare a thing it is to contemplate such a person. How few we produce in this restoration of the Gospel. We remain as a people too low, too mean, too vulgar, too condescending to be called of God. No wonder we stumble and fall backward and many are taken in snares. (Isa. 8: 11-17.)