The Puritans believed that they would be able to establish a pure church in the colonies, in the lands known as New England,  that would offer a model for the churches in England and reform the Anglican Church and cleanse it of any vestiges of the hated Catholic religion. Refer to Religion in the Colonies

Great Migration - Separatists
The Separatists were a group of Puritans who advocated total withdrawal from the Church of England and wanted the freedom to worship independently from English authority - the first Separatists to migrate to America were the Puritans, or Pilgrims, who travelled on the Mayflower and landed in America on December 21, 1620.

Reasons for the Great Migration - Religion in England
During the period between 1620 and 1640 England was in religious turmoil. The religious climate was so hostile and threatening that many Puritans were forced to leave the country, many of whom fled to the Netherlands. Religion in England was dictated by the monarchy. King James I (19 June 1566 – 27 March 1625) was a Protestant  and during his reign the English colonisation of North America began with the foundation of Jamestown, Virginia, in 1607. The Puritans presented him with the Millenary Petition requesting reforms in the Anglican church, particularly the abolition of confirmation, wedding rings, and the term "priest". King James I banned religious petitions starting a sense of persecution among the English Puritans. The situation became far worse when King Charles I (19 November 1600 – 30 January 1649) ascended the throne in 1625. King Charles I had a Catholic wife and leaned towards the Catholic religion. The Puritans were classed as dissenters and persecuted for their beliefs. The scene was set for the Great Migration.