The New Covenant (νέα Διαθήκη - Néa Diathíki) is the formal agreement made by God with humanity that has succeeded the Old Abrahamic Covenant. It, unlike the Old Covenant, removes personal connection to one's sins, replacing the act of personal and annual atonement with a new relationship with God via an intercessor on humanity's behalf. This intercessor is believed by Christians to be Jesus Christ.
The New Covenant itself was introduced to humanity via the prophets Moses, Ezekiel, and Jeremiah, while the Old Covenant with Israel was still in effect. During Moses' time, it was alluded to as the time when God would "circumcise" hearts. Ezekiel prophesied that God would give the Israelites hearts of flesh, and that they would all be guided by His Spirit so that they would follow His law, while Jeremiah prophesied that God would forget His People's sins, and that they would all in time be forgiven.
Jesus Christ established the New Covenant during His Ministry, with the Great Commandment of Love for God and humanity, and the New Commandment that all of His Disciples were to love one another. In the Last Supper, He revealed that the New Covenant would be sealed in His blood, and that they were to repeat the Eucharist in His memory.