Blessed are the pure in heart, for they shall see God.

In the Bible, the heart refers to the inner life of man. It refers to the will, the emotions, the intellect and our moral character. Jesus’ says that members of the kingdom are pure in heart.
Jesus emphasized purity of heart because the religious community of his time satisfied themselves with mere external and perceived holiness. Look at Matthew 23:23-28.

23 "Woe to you, scribes and Pharisees, hypocrites! For you tithe mint and dill and cumin, and have neglected the weightier matters of the law: justice and mercy and faithfulness. These you ought to have done, without neglecting the others. 24 You blind guides, straining out a gnat and swallowing a camel! 25 "Woe to you, scribes and Pharisees, hypocrites! For you clean the outside of the cup and the plate, but inside they are full of greed and self-indulgence. 26You blind Pharisee! First clean the inside of the cup and the plate, that the outside also may be clean. 27 "Woe to you, scribes and Pharisees, hypocrites! For you are like whitewashed tombs, which outwardly appear beautiful, but within are full of dead people's bones and all uncleanness. 28 So you also outwardly appear righteous to others, but within you are full of hypocrisy and lawlessness.

The Pharisees were more concerned about looking good to others than actually being good people. They lived their lives seeking the praise of men and not the praise of God. Jesus was very tender and merciful to those that realize their sin and don’t try to excuse it. He was gracious and forgiving to those that admitted their need of forgiveness and wanted to change. However, to the self-righteous, to those that made a phony, external show of righteousness, he denounced them.   
To be ‘pure in heart’ means to have inner moral integrity. It is a sincere, authentic disposition that moves the disciple to pursue righteousness and compels him to live obediently. Our actions spring from our heart. If we are pure in heart, then we will seek to live obediently to God. However, purity of heart is not a qualification for salvation. Instead it is a result of salvation. In other words, like the other beatitudes, we do not merit heaven by first obeying this beatitude. Rather, we reflect this beatitude, because we have already been secured in heaven.
We do not conjure up purity on our own. God does this work in us. Notice what David says in Psalm 51:7, “Purge me with hyssop, and I shall be clean; wash me, and I shall be whiter than snow.” God is the one that does this. Again in verse 10, “create in me a clean heart, O God, and renew a right spirit within me.” Again, God is the one that does this. He does it by first enabling us to believe the Gospel. In order to believe, we must first have received new life from God. God also does this by giving us the Holy Spirit. It is the work of the Spirit to clean out our hearts. In fact, Jesus is already saying that we do have pure hearts.
This is significant because what he is saying is that the New Covenant was being fulfilled in his ministry. This New Covenant promised forgiveness of sins and inner transformation. Look at Ezekiel 36:25-27,

25 I will sprinkle clean water on you, and you shall be clean from all your uncleannesses, and from all your idols I will cleanse you. 26 And I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh. 27 And I will put my Spirit within you, and cause you to walk in my statutes and be careful to obey my rules.    

God is the one that does all of this. This means that if we are to have purity of heart, we must trust God to do it. He does it through the preaching of the Gospel and through the sacraments. A pure heart manifests itself in genuine obedience to God from the inside out!
Jesus says that those who are pure in heart “shall see God.” This is the future reward for those with pure hearts. It is the promise of heaven. The purity God works in us will one day be perfected. This happens when we die. At death, God immediately purges us from all sin and brings us home to heaven.