The roughly twenty years of Puritan migration to New England was a result of religious differences back in England; in short, the Puritans wanted to "purify" the church, as the story goes, earning them their name. Whether or not that is how they acquired their name, this group of Protestants did believe that reforms to the Church of England had not gone far enough and that it still retained too many characteristics of the Catholic church.
The popular story for younger children is that the Puritans came seeking religious freedom; actually, they came seeking religious freedom the way they practiced it, and kept themselves fairly busy investigating potential witches, persecuting Quakers and running uncooperative Puritans out of the colony. Despite a difficult and work-intensive lifestyle, and occasionally tumultuous relations with England, economically, the colony did well. Although it initially depended heavily on staples imported from England, shipbuilding and fishing industries grew quickly and the community prospered to such an extent that some church officials became unhappy with the increasing presence and display of material goods and tried unsuccessfully to regulate these possessions.