A Congregational church is by the institution of Christ... a company of Saints by calling, united into one body by a holy covenant, for the public worship of God, and the mutual edification of one another, in the Fellowship of the Lord Jesus.
Cambridge Platform (1648), ch. II, s. 6.
Congregationalism began in the late sixteenth century in England. The Church of England had broken away from the Roman Church and was beginning to adopt Reformed doctrine. There was widespread disagreement, however, regarding how the Church should be run. Some supported episcopalism, where authority flows top-down, while others promoted a presbyteral polity, where authority flows back and forth from top to bottom.
A third group, however, insisted that church authority flow from the congregation upward - that there is no authority over a church except for the lordship of Jesus Christ. These Puritans, so-called for wanting to "purify" the Church, found their way to the Plymouth and Massachusetts Bay Colonies, where they began the great experiment known today as Congregationalism.
Authority in the local Congregational church is vested in the congregation - in the people. This means that all practical decisions, such as calling and ordaining clergy and church officers, maintaining an order to worship, authorizing missions, or supervising building projects, are discussed and voted upon by the congregation, rather than passed down from a diocese or ratified by a conference.
This does not mean that the local church can invent its own beliefs, for we recognize one authority above us: the Lord Jesus Christ our King. The autonomy of the local church cannot supersede the Word of God, which was made flesh in Christ.
This also does not mean that local churches should be isolated and left to themselves, for it is good and healthy to maintain fellowship with neighboring churches - just as our church members covenant with each other to share fellowship. The First Church in Weymouth is a member of two associations of Congregationalist churches: the Massachusetts Association of Congregational Christian Churches (MACCC) and the United Church of Christ (UCC).