Supersessionism is the teaching that New Covenant established by Jesus replaces the Old Testament Mosaic covenant.  The word is derived from “supersede.” So, basically, it asserts that the Christian church has replaced Israel.  It is also sometimes called Replacement Theology.  Since national Israel failed to recognize the Messiah and therefore failed to carry out the mission of proclaiming the Messiah, Jesus, to the world, God moved to the Gentiles to accomplish his will. Israel broke the covenant of God with them. Gentiles are grafted in, adopted into the plan of God. However, God is not done with Israel.

“For I do not want you, brethren, to be uninformed of this mystery—so that you will not be wise in your own estimation—that a partial hardening has happened to Israel until the fullness of the Gentiles has come in; 26 and so all Israel will be saved; just as it is written, “The Deliverer will come from Zion, He will remove ungodliness from Jacob,” (Romans 11:25–26).