The following explanation comes from the book, "Meet the Puritan's" by Joel R. Beeke and Randall J. Pederson:
The Puritans [were] burning and shining lights. When cast out by the black Bartholomew Act, and driven from their respective charges to preach in barns and fields, in highways and hedges, they in a special manner wrote and preached as men having authority. Though dead, by their writings they yet speak: a peculiar unction attends them to this very hour; and for these thirty years past I have remarked, that the more true and vital religion hath revived either at home or abroad, the more good old puritanical writings, or the authors of a like stamp who lived and died in communion of the Church of England, have been called for.... Their works still praise them in the gates; and without pretending to a spirit of prophecy, we may venture to affirm that they will live and flourish, when more modern performances of a contrary cast, notwithstanding their gaudy and tinseled trappings, will languish and die in the esteem of those whose understandings are opened to discern what comes nearest to the scripture standard. -George Whitefield, Works, 4:306-307
Just what is meant by the term Puritan? Many people today use the term to describe a morose and legalistic brand of Christianity that borders on fanaticism. Much of this stereotype was the product of the nineteenth-century anti-Puritan sentiments. While subsequent cultures have expressed various opinions of the Puritans, it is helpful to chronicle a brief history of the term and to assess the movement as objectively as possible.
The term Puritan was first used in the 1560s of those English Protestants who considered the reforms under Queen Elizabeth incomplete and called for further "purification" (from the Greek word katharos, "pure").
...the Puritans embraced five major concerns and addressed each of them substantially in their writings:
The Puritan sought to search the Scriptures, collage their findings, and apply them to all areas of life. In so doing, the Puritans also aimed to be confessional and theological, and drew heavily on the labors of dedicated Christian scholarship.
The Puritans were passionately committed to focusing on the Trinitarian character of theology. They never tired of proclaiming the electing grace of God, the dying love of Jesus Christ, and the applicatory work of the Holy Spirit in the lives of sinners. Their fascination with Christian experience was not so much motivated by an interest in their experience per se as it was in their desire to trace out the divine work within them so that they could render all glory to their Triune Lord.
In common with the Reformers, the Puritans believed in the significance of the church in the purposes of Christ. They believed therefore that the worship of the church should be the careful outworking and faithful embodiment of her biblical faith, and so Puritanism was a movement that focused on plain and earnest preaching, liturgical reform, and spiritual brotherhood. Likewise, the Puritans believed that there was an order or polity for the government of the church revealed in Scripture, and the well-being of the church depended on bringing her into conformity to that order.
In the great questions of national life presented by the crises of their day, the Puritans looked to Scripture for light on the duties, power, and rights of king, parliament, and citizen-subjects.
In regard to the individual, the Puritans focused on personal, comprehensive conversion. They believed with Christ that "except a man be born again, he cannot see the kingdom of heaven" (John 3:3). So they excelled at preaching the gospel, probing the conscience, awakening the sinner, calling him to repentance and faith, leading him to Christ, and schooling him in the way of Christ. Likewise, the Puritans believed with James that "faith, if it hath not works, is dead being alone" (James 2:17). So they developed from Scripture a careful description of what a Christian ought to be in his inward life before God, and in all his actions and relationsips in this life, at home, in the church, at work, and in society.