What is the historical significance of "The Crucible"?

There are several aspects of this play of historical significance, the first being the reason it was written.  Arthur Miller wrote this as a counterattack for being forced to testify before the House Committee on Un-American Activities in 1956, at the height of the McCarthy/Red Scare era. The story of the witch-hunt at Salem was used as a framework for a moral assault on political witch-hunts.

The second significant aspect is that it brings an episode in American history to light that we should be aware of.  It is all too easy to believe the worst of others, and to be swayed by momentary feelings or simply bad ideas.  The people of Salem in the real witch trials went overboard by a long shot.

On the other hand, if we looks closely at the real incident and the records of the time we see another lesson.  The play is after all fictitious, not a true reporting of the events, and the characters are not at all historically accurate.  Abigail Williams and John Proctor did not have an affair, and she was not in love with him.  He was noted as a bad-tempered master who beat her.  Tituba and her husband, John, were not black but Carribean Indians, and they were slaves.  Tituba did teach some voudoun-like "magic" to the girls, and hysteria and guilt did the rest.  The clergy did not support the trials, and in fact they appealed to the governor to suspend the proceedings.  At least five of those executed traded on reputations of occult powers, and at least one freely admitted when first asked that she practiced witchcraft.  The barest outline of the Salem situation is used as a framework from which to hang a story of political hysteria and opportunism.

We tend to forget today that in the 17century most people believed in witchcraft, and witchcraft in fact was practiced widely in Europe and the colonies.  It may have no actual power, but to people who believe in it it's frightening.  Thousands were put to death in Europe in the same period, and there were witchcraft trials in New England before and after Salem.  So a third point of historic significance is that we must remember that however laudable the intent of fictionalizing history for entertainment, it does make the story fiction.  I strongly suggest reading Witchcraft at Salem by Chadwick Hansen, an exhaustive study of the records and history of the trials, and of how we ended up with the story as it is perceived today.