The Puritans believed the Anglican Church, led by the King of England, had developed a hierarchy much like the Catholic Church they had separated from originally. So unlike Anglicanism, there were no Bishops and Archbishops, and no dominating structure for the church in general. Puritans wanted each congregation in the various villages of Massachusetts to be self-sustaining and autonomous. Puritans feared extensive heirarchy would corrupt them as it had, in their view, the Catholic and Anglican churches.
Puritans also believed in Calvinism (teachings of John Calvin), that a person's fate in the afterlife had been predetermined, and that only living as godly a life as possible would enable you to receive the Grace of God and entry into the Kingdom of Heaven.
Lastly, I would say there was much more extensive social pressure and control among the small Puritan villages than there was in Anglican dominated regions in Britain. It was this fear of being ostracized or condemned by the Puritan village that often defined their daily lives.