Puritanism was a set of religious beliefs that sprang up in England in the years after the Protestant Reformation and the creation of the Church of England. The Puritans were given this name because they wished to "purify" the Church of England, purging it of all vestiges of Roman Catholicism. They believed that the Catholic Church was too hierarchical and relied too much on ceremony.
Puritan beliefs were basically Calvinistic. They believed in predestination and in salvation solely through the grace of God. They believed that there was nothing any person could do to deserve salvation.
Puritans also believed in a close connection between religious and secular matters. They believed that God had made a covenant with them that required them to exhibit correct behaviors so as to prevent God from punishing their society. This meant that they used secular government to enforce church teachings.