The Puritans originated in Europe during the Reformation. They were so named because they wanted to further purify the Church of England, the Anglican Church. They believed that the Anglican Church was still too much like the Catholic Church and needed further reform. They were considered extremists. Since they faced persecution in England, a group of them decided to form a settlement in the New World, so they sailed to the new world over a period of years. They are also referred to sometimes as Separatists because they wanted to "separate" from the Anglican Church.
When they got to America, they formed colonies in Plymouth Bay and elsewhere in New England. We refer to them as "The Pilgrims" in American history. Life in Puritan New England was harsh. The Puritan beliefs were very strict. They had a strict interpretation of the Bible and believed they should live a pure life, free from sin. The problem was that no man can live free from sin. We are all sinners. The only perfect man to live sinless was Christ. Naturally, then, a lot of hypocrisy popped up in Puritan New England. Many Puritans preached one thing publically, but lived a very different life behind closed doors.
This religious hypocrisy became the subject matter for many works of literature during latter years in American literature - The Scarlet Letter, and many short stories by Nathanial Hawthorne are good examples - The Minister's Black Veil, Young Goodman Brown, etc.
The Salem Witch Trials were seen to be an outgrowth of the impossibility of living under such strict rules. The Puritans became so intent on purity, they were capable of degenerating into hysteria.
I am assuming you are looking for information on how Puritan society affected literature. You could write a book on this subject alone.
If you do some digging, you will find many, many online resources from universities and, perhaps of more help to you, from high school teachers who have created webquests, etc. and are willing to share with other scholars. Here are some good links below. There is good information right here on eNotes!