The setting—both the time period and physical place—are crucial to Arthur Miller's plot in The Crucible. The events of the play could not have happened in this way in any other place. However, it is well-known that Miller wrote The Crucible as a kind of allegory in reference to the Red Scare and McCarthy investigations into supposed American communists. That historical event was, to Miller, another sort of "witch hunt," while the play's 17th-century Salem setting depicts the famous actual witch hunt of the colonial period.
The Puritan community of colonial Salem, Massachusetts is depicted as strict and superstitious. Miller's characters live in a world of rigid requirements, where many activities are banned and considered unholy. In this world, any transgressions or rebellions would be considered "witchcraft," almost in the sense that identifying someone as a witch was like saying that the person was simply "different" or did not follow the society's strict rules. In this strange new world, it was perhaps natural for the colonists to be fearful and superstitious. The witch hunt could be seen as a way to control the chaos of the unknown that was very much a part of daily life.
The basic plot of The Crucible is that a few of the daughters of the prominent Puritan townsfolk are caught dancing in the woods with a slave named Tituba. This basically looks like a satanic ritual. In order to protect themselves and hide their own transgressions, the girls begin to lash out at other members of the community by accusing them of being witches. For example, Abigail names Elizabeth Proctor as a witch after having an affair with Elizabeth's husband, John Proctor. Eventually, a witch investigator comes to Salem and the girls accuse Tituba of being a witch and of having contacted the devil. The girls even pretend to be possessed by the supposed witches during their trials, and there is really no way to prove that what they say is happening is not actually happening. Again, these girls project their own guilt onto others as a means of self-preservation. Their actions have very serious consequences, and some townspeople are even put to death as witches. The setting is inherently linked with this plot because the hysteria that ensues is directly tied to the religious beliefs of the townspeople, the superstitions of their faith, and the unknown setting of the "New World."