 The Pilgrims themselves were a subset of an English religious movement known as Puritanism , which sought to " purify " the Anglican Church of its " Catholic " trappings . The movement sought to return the church to its original state and to practice Christianity as was done in the times of the Apostles . Following Martin Luther 's and John Calvin 's Reformation , Puritans believed that the Bible was the only true source of religious teaching and that any additions made to Christianity had no place in Christian practice , especially with regard to church traditions , such as clerical vestments or the use of Latin in church services . In particular , they were strongly opposed to the Anglicans ' episcopal form of church government . They believed that the church was a community of Christians who made a covenant with God and with one another . Their congregations had a democratic structure . Ministers , teachers , and lay church elders were elected by and responsible to the entire congregation ( Calvinist Federalism ) . Each congregation was independent of all the others and directly subject to God 's ( or Christ 's ) government ( theocracy ) , hence the name Congregationalism . The Pilgrims distinguished themselves from the Puritans in that they sought to " separate " themselves from the Anglican Church , rather than reform it from within . It was this desire to worship from outside of the Anglican Communion that led them first to the Netherlands and ultimately to New England . 
