Plymouth colony was founded as a haven for English Puritans who wanted to practice their form of worship without fear of persecution. The Puritans--who were very influenced by the earlier work of the Scottish Reformer John Knox--believed the Anglican Church (a Protestant denomination which was the official church in England) was corrupt. They initially sought to purify it--hence the name "Puritans"--but Puritan congregations began to experience sporadic persecution from the Anglican Church.
As a result of this persecution, some congregations began contemplating leaving England altogether. The Reverend John Robinson and William Brewster led their congregation across the English Channel to Leyden, Holland, where they hoped they could put down roots. Holland offered religious toleration, but Holland proved a poor home for the Puritans because non-Dutch were barred from the crafting guilds; this meant the Puritans could only perform manual labor. The Puritans also believed the Dutch children were a bad influence.
The Puritans began to look for somewhere else to move; they decided on the New World. They originally contracted with the Virginia Company to settle within Virginia, but they were blown off course on their voyage and ended outside of the Virginia territory. Thus, they drafted the Mayflower Compact to serve as an organizing principle and they founded the town of Plymouth.