Replacement theology is the teaching that the Christian church has replaced national Israel regarding the plan, purpose, and promises of God.
Therefore, many of the promises that God made to Israel must be spiritualized. For example, when it speaks of Israel being restored to the land, this really means that the Christian church will be blessed. Also, covenants made with Israel are fulfilled in the Christian church so, for example,
- The Jewish people are no longer God's chosen people. Instead, the Christian church now makes up God's chosen people.
- In the New Testament after Pentecost, the term "Israel" refers to the church.
- The Mosaic covenant (Exodus 20) is replaced by the new covenant (Luke 22:20).
- Actual circumcision is replaced by a circumcision of the heart (Rom. 2:29).
So, in replacement theology the church has replaced Israel as the primary means by which the world is blessed by God's work. Though it is true that the church does replace Israel in some areas such as properly representing God on earth, acknowledging the promise of the Messiah, etc., it is not Biblical to say that God is completely done with Israel and that the Christian church is its complete replacement.
"For I do not want you, brethren, to be uninformed of this mystery, lest you 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 thus all Israel will be saved; just as it is written, 'The Deliverer will come from Zion, he will remove ungodliness from Jacob,'” (Rom. 11:25-26).
Some replacement theologians would teach that any mention of "Israel" after Acts chapter 2 (Pentecost) would be referring to the Christian church, but the above Scripture cannot be used to support that idea. In fact, it plainly contradicts it. Obviously, God is not done with Israel. The text tells us that God has hardened Israel, but it also tells that disheartening is temporary.
Replacement theology is also known as supersessionism which means that the Christian church has superceded Israel in God's plan.