The Crucible was written in response to a particular conflict from the 1950s and drew on an even earlier conflict from the 17th century.
The earlier conflict to which you refer is the Salem Witch Trials. Miller's play takes its plot from these historical trials. Reverend Parris was an actual person who led his community to mass hysteria, causing the death of twenty people. Many of these people died because they refused to take part in the trials and were condemned to death for their refusal. This period of time is one of the most shameful in American history.
After World War II, fear of Communism was rampant in American society. Some of our leaders and other Americans linked the American Communist Party with Communist Russia. Senator Joseph McCarthy set up the House Un-American Activities Committee which held hearings to question any Americans who had, or might have had, any connection to the American Communist Party. McCarthy developed a list of those people he felt were a threat to national security. Especially hit hard was the artistic community that developed films and music in Hollywood. Each person called before the Committee had to tell their involvement with Communism, but more importantly, they had to name others who might also be involved. When people refused to participate in the hearings, they were "blacklisted", which meant they wouldn't be hired by anyone for fear of being accused themselves. Miller saw this hysteria as the same kind that gripped Salem, Massachusetts in the 1600s.