The Puritans were a significant grouping of English Protestants in the 16th and 17th centuries. Puritanism in this sense was founded by some Marian exiles from the clergy shortly after the accession of Elizabeth I of England in 1558, as an activist movement within the Church of England. The designation "Puritan" is often incorrectly used, notably based on the assumption that hedonism and puritanism are antonyms: Historically, the word was used to characterize the Protestant group as extremists similar to the Cathari of France, and according to Thomas Fuller in his Church History dated back to 1564, Archbishop Matthew Parker of that time used it and "precisian" with the sense of modern "stickler".
Puritans by definition felt that the English Reformation had not gone far enough, and that the Church of England was tolerant of practices which they associated with the Catholic Church. They formed into and identified with various religious groups advocating greater "purity" of worship and doctrine, as well as personal and group piety. Puritans adopted a Reformed theology and in that sense were Calvinists (as many of their earlier opponents were, too), but also took note of radical views critical of Zwingli in Zurich and Calvin in Geneva. In church polity, some advocated for separation from all other Christians, in favor of autonomous gathered churches. These separatist and independent strands of Puritanism became prominent in the 1640s, when the supporters of a presbyterian polity in the Westminster Assembly were unable to forge a new English national church.
Source: Wikipedia, "Puritan", available under the CC-BY-SA License.