In the Old Testament, God made an agreement – a Covenant – with His people. This First Covenant was given to Moses alone to the Hebrew People. With the Old Covenant, God would also agree to give the Hebrews the promised land if they would follow His Commandments and offer the Sacrifices. With the New Covenant, God Himself through His Incarnation as Jesus Christ, God promises us His Heavenly Kingdom if we follow His Commandments and participate in His Sacraments.
The Old Covenant was written on tablets of Stone but the New Covenant is written on our Hearts. When we are Baptized and Chrismated we receive a spiritual gift. We receive the Holy Spirit who remains in our hearts and informs us how we should behave as the sons and daughters of the Most High. Our actions always follow our thoughts and emotions. We are to observe any thought or emotion not befitting to a child of God and we must then fight to cleanse it from our hearts and our minds. Sincere frequent participation in Sacraments and acts of charity with humility are the tools the Lord gave us to cleanse ourselves from all such impure attacks. If we do this, we will reach the state where we do good deeds and our left hand will not know what your right hand is doing (Matthew 6:3), because we will have returned to our original state where doing a good deed is instinctual and natural to us. This is the purpose of the New Covenant, to heal us restoring us to our original state as Adam and Eve where in the Garden and to bring us to the state that Christ is after his bodily Resurrection.