In order to understand the meaning of replacement theology (also referred to as Supersessionism), it is necessary to contrast it with its rival system called dispensationalism. Both systems come to different conclusions regarding a variety of issues such as whether or not the Jews are still God’s chosen people.
The Replacement Model
In the replacement theology model of understanding scripture, supported by early church "fathers" such as Justin Martyr and Origen, God has changed his chosen people from ancient Israel to the New Testament Church.
The replacement theology model, therefore, asserts that "the chosen" can include not only Israelites but also Gentiles (non-Israelites) as well. This model also teaches the covenant God made with Israel at Sinai (the Old Covenant) has been abrogated by the New Covenant delineated in the New Testament.
In a variation of the replacement model, the Roman Catholic Church believes that it is the "new Israel" who has superseded the Old Testament's chosen people.
The Dispensationalism Model
Dispensationalism, as opposed to replacement theology, states that God is not yet done with Israel as his chosen people.
Now then I say, did God Himself repudiate His people? MAY IT NEVER BE! For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin. (Romans 11:1, HBFV).
Dispensationalism believes the Jews, or even Israelites in general (including what many refer to as the "Lost" tribes of Israel), are still God's people.
Today, one of the chief ways this theology (and dispensationalism) becomes politically controversial is when Christians take sides concerning the legitimacy of the modern state of Israel in the Middle East.
While replacement theology has and continues to be widely held by those who consider themselves Christians, a number of denominations are either moving away from or have rejected this template for understanding scripture.