From the Wikipedia article on Churches of Christ
Members of the church of Christ do not conceive of themselves as a new church started near the beginning of the 19th century. Rather, the whole movement is designed to reproduce in contemporary times the church originally established on Pentecost, A.D. 33. The strength of the appeal lies in the restoration of Christ's original church.— Batsell Barrett Baxter
Churches of Christ are autonomous Christian congregations associated with one another through common beliefs and practices. They seek to base doctrine and practice on the Bible alone in order to be the church described in the New Testament. Churches of Christ teach that God saves and adds to the church those who hear the gospel, believe in Christ, repent of sin, confess Jesus Christ as the Son of God, are baptized for the remission of sins (Acts 2:36-38, 47; Rom. 10:9-10) and live according to God's will.