The term Matthew used here means pure or “clean.” It can be used literally of physical cleanness, but Scripture often uses it for moral cleanness and purity. A simple but helpful way of looking at the word is to realize that it implies the absence of impurity or filth. It implies a singleness of purpose, without distraction (akin to the concept of “holiness,” being set apart for a special purpose; see Jas. 4:8). Any distracting or corrupting influence a kingdom servant allows into his or her heart makes that person less effective as a servant. The kingdom servant has a heart that is undivided and unalloyed.
This quality is a natural by-product of the preceding blessings and character qualities. Purity of heart is not manufactured by the believer, but is granted by the God of mercy (5:7) to those who mourn their spiritual bankruptcy (5:3–4) and who seek his righteousness (5:6). When the king grants purity of heart, he gives not only judicial purity (forgiveness, absolution from guilt), but also the actual removal of corrupting impurities from the heart. This comes about through the empowerment of the believer to grow into holiness and out of these impurities.
Jesus may have had a dual meaning behind the phrase ‘see God.’ First, the pure heart is unhindered in its ability to understand the heart and person of God in this life on earth and, in this sense, is better able to see God. Moreover, only the pure (forgiven) heart is able to enter heaven to enjoy the presence of God for eternity.
Weber, S. K. (2000). Matthew (Vol. 1, p. 60). Nashville, TN: Broadman & Holman Publishers.