Puritan means moralistic, rigid, austere. It is an adjective used to designate that person rigorous in the application of moral principles, ideas and customs, specifically regarding sexual behavior. It's that follower of Puritanism.
Puritan Revolution
Puritanism was a Protestant doctrine based on Calvinism, guided by strict moral principles and simple form of worship practiced in England during the 16th century, in that the precepts were based on pure Christianity, following more rigorous standards of conduct than those normally in force.
Calvinism considered the Eucharist mere commemoration of the Last Supper of Christ, eliminated the ritual and instrumental music in the mass, stripped the churches of stained glass, paintings and images, reduced the service to a sermon between four walls, devoid of loud. It abolished the Easter and Christmas celebrations, and erased all traces of the episcopal system: the congregations they should choose their own elders and preachers, while a superior college of ministers would govern the Church.
Puritans who professed Puritanism in England were persecuted by the Stuart Dynasty, which led a large part of its adherents to emigrate to America.