Purity is an important part of the Old Testament. The devout Jewish believer was constantly being reminded of this requirement for the worship of the one True God. The vessels for the Temple had to be pure and of the best quality, the sacrifices he brought must be pure and without spot or blemish, he himself was to be kept pure if he were to be able to come to the Temple, uncontaminated by dead bodies, unclean food or unclean people. By Jesus day, it had gotten to be a really big thing for the Pharisees, they would not even pass by a grave, or get within a certain distance of a person they considered unclean. They were constantly concerned with being "ritually pure". But in this Beatitude, Jesus stressed that what God really values is inward purity, purity of the heart.
David, that man after God's own heart, understood the importance of purity of the heart. As you read the Psalms, you find David talks quite a bit about it. For instance in Psalms 19:14 - "Let the words of my mouth, and the meditation of my heart, be acceptable in thy sight, O Lord, my strength, and my redeemer." David knew that inward purity was important, that the thoughts of his heart needed to be "acceptable" to God as well as the words he spoke aloud to others. He also knew that he himself would need help with this cleansing of his thoughts. His prayer was: "Create in me a clean heart, O God, and renew a right spirit within me." (Psalm 51:10). It is a lot easier to appear clean on the outside than to really be clean on the inside.
Clean living, a spotless reputation, an appearance of Holiness without the stain of sin, these are attainable if you really work at them. The Pharisees of Jesus day had it down to an art form. However, Jesus called them out on the things that no one could see. He said: "Woe to you, teachers of the law and Pharisees, you hypocrites! You are like whitewashed tombs, which look beautiful on the outside but on the inside are full of the bones of the dead and everything unclean." (Matthew 23:27 NIV) Jesus emphasizes what David wrote about, that you can look "beautiful on the outside" but be full of "everything unclean" on the inside.
Being "pure in heart" is a difficult thing to maintain. You will need to be like the most dedicated of housekeepers, whisking away each day, by prayer, the dust that might settle in the corners of your heart. Being watchful for even the slightest thing that might clutter up your mind with thoughts that could lead to inward sin, asking God's help with all of it in "prayer and supplication". David put it this way in Psalm 19:12: "Who can understand his errors? cleanse thou me from secret faults." And he continued in verse 13 with these words in his prayer to God: "Keep back thy servant also from presumptuous sins; let them not have dominion over me". Is it any wonder David was called a "man after God's own heart"? What would happen if we prayed these prayers like David prayed, daily or even hourly if needed? Would we become "men and women after God's own heart" as well? Perhaps that is the ultimate expression of being "pure in heart".
So what was promised to the pure in heart? Jesus said they would "see God". Well, one day the Bible says we would all see God at the time when "every knee shall bow" (Philippians 2:10-11). So it must be more than just seeing God on judgement day or being in His presence in Heaven. The greek word used in Matthew 5:8 literally means to "stare at" or to "discern clearly". What is implied is that the "pure in heart" will be able to discern God clearly here on earth. How could that be? John put it this way: "God is light; in him there is no darkness at all. If we claim to have fellowship with him and yet walk in the darkness, we lie and do not live out the truth. But if we walk in the light, as he is in the light, we have fellowship with one another, and the blood of Jesus, his Son, purifies us from all sin." (1 John 1:5-7 NIV). Fellowship, companionship with God? What a wonderful blessing this implies! We will literally be able to 'see' Him everywhere. In the first part of Psalm 19, David starts his song out with these words which reveal to us the happiness and fulfillment he found in his own close relationship with God:
"The heavens declare the glory of God; the skies proclaim the work of his hands. Day after day they pour forth speech; night after night they reveal knowledge."
"Two grains of quicksilver laid upon a polished surface will never unite if their surfaces be dusted over with minute impurities, or if the surface of one of them be. Clean away the motes, and they will coalesce and be one. A film of sin separates men from God. And if the film be removed the man dwells in God, and God in him" (MacLaren's Expositions)