In "The Crucible," Miller uses the historical account of the Salem witch trials as an historical narrative and this is also an allegory for present day (then, 1953) America.
In 1692, in Salem, Massachusetts, a girl named Anne Putnam accused others of consulting with the devil. A man named Samuel Parris led the prosecution, leading to 20 executions. Many interpret "The Crucible" as a commentary on McCarthyism, a similar witch hunt during the late 1940s through the late 1950s. However, instead of an actual witch hunt, McCarthy and his followers were accusing certain citizens of having communist leanings. Like the witches who were brought to court, those accused of communist sympathies were brought before the House Un-American Activities Committee to answer, admit, deny, and/or name other communist sympathizers.
Although the play is based on historical people and events, Miller writes in a note preceding Act One that:
This play is not history in the sense in which the word is used by the academic historian.
To be sure, many facts were changed and Miller goes on to say how some characters were fused into one and he cites other departures from the actual history which were necessary to make the play more dramatic and engaging. This dramatization was to highlight what Miller called one of "the strangest and most awful chapters in human history."
Miller does not mention McCarthyism as the parallel to the Salem witch hunt in the introductory note. But given that the play was written in 1953 and that Miller knew writers who were summoned to appear before the House Un-American Activities Committee, the connection is obvious. Miller paid close attention to the language of 1692 Salem in order to give the drama historical credibility. Therefore, Miller used the dramatic account of the historical Salem witch trials as a general allegory and this was widely interpreted as a particular allegory of the hearings led by Senator Joseph McCarthy.