"Puritan" was a term of opprobrium, and no one actually used it to describe themselves, except in an ironic fashion. For example, William Bradshaw's English Puritanisme (1605) was written as a defence of the views associated with what historians now term "Puritanism", although Bradshaw considered the name to be "odious and vile."

(At the risk of violating the subreddit rules, an analogy might be drawn to the use of the term "SJW" today, which is used to insult people of a certain political bent who don't use the term themselves.)

But historians have subsequently used the label as a shorthand for a constellation of religious and political attitudes: a Calvinist belief in the division between the elect and the damned, a suspicion of ceremonies, an emphasis on preaching, and fierce anti-Catholicism.

These religious questions were explosive political issues in the 17th century because of the absolutist and Arminian tendencies of the Stuart kings, particularly Charles I. At this time, it was generally believed that an established church was a keystone of national unity, and religious tolerance was associated with political strife. The Stuarts and their ministers consequently stubbornly promoted a prelacy and liturgy that was at odds with the beliefs of the so-called Puritans, who responded by migrating to America or taking up arms during the English Civil War.

By the 1640s, the term was used with decreasing frequency; many used the labels "Presbyterian" or "Independent" instead. But the real death knell of the term came with the passage of the 1689 Toleration Act, which granted toleration to Protestants who dissented from the Anglican Church - including the Congregationalists of New England, who were the descendants of the first settlers historians now call "Puritans". Once the Act was passed, the religious questions that had caused such passionate strife earlier in the century became less politically contentious.

By the time of the War of Independnece, the great majority of New Englanders attended Congregationalist churches - but the religious difference that mattered at the time of the Revolution was the split between New Lights and Old Lights that arose during the First Great Awakening beginning in the 1730s.

On the term "Puritan", see C.H. George, "Puritanism as History and Historiography," Past and Present, 41 (1968); Michael G. Finlayson, "Puritanism and Puritans: Labels or Libels?" Canadian Journal of History, 8 (1973).