Puritans were comprised of various groups and sects that arose in England in the sixteenth through seventeenth-centuries. They believed the English Reformation had not moved far enough from Roman Catholic doctrine and practice to be the true faith.
Sola Scripture was a foundational Puritan belief. The term means "only scripture." Its premise is and was that only the Bible has authoritative weight as a theological guide. The Puritans believed that heresies or mistakes had crept into Roman Catholic and Anglican theology, which were leading innocent believers badly astray. Therefore, the Puritans put their faith entirely in the Bible. If a practice or idea was not in the Bible, they rejected it.
Sola Scripture led to individual examination of conscience, another Puritan belief. Puritans put no faith in confessing to a priest. Sin was a matter between the individual and God. One prayed directly to God for moral guidance. This led to an emphasis on personal, rather than corporate (group) prayer. It led also to spiritual autobiography, as Puritans, such as John Bunyan in his Grace Abounding to the Chief of Sinners, published their records of spiritual struggles for the edification of other believers.
Simplicity was a Puritan practice, and one that distinguished the Puritans visually from other groups. Puritans thought places of worship, as well as dress and housing, should be simple, believing that a sign of the corruption and secularization in the Church of England and Roman Catholicism could be found in all the glitter, gold, pomp, and finery of churches, clergy, and worship. The Puritans wanted to strip the excess away to find the primitive, core faith.
Puritans believed too that power in the church came from the bottom up, not the top down. For example, Presbytarian ministers were chosen by the congregation and lay elders had a good deal of power. This may not seem important to us, but at the time, it was a radical concept and one considered dangerous in a hierarchical society, in which power was traditionally conceived as top down, coming through God to king, bishop, and aristocrat.