The Crucible examines the witch hunts that took place in 17th century Salem, Massachusetts. When he wrote it, Arthur Miller was already a successful playwright. The play also subtly refers to the 'communist witch hunts' in the USA in the 1950s.
During the 17th century in Salem, Massachusetts, there really were witch hunts very much like those depicted in this play. Early settlers in North America had fled from religious persecution in England and other European countries but this did not make them more tolerant. They were very intense about religious purity. By modern standards we might call them religious fanatics. They were very intolerant of 'alternative viewpoints.'
Arthur Miller was born in 1915 in New York. His Jewish parents were both immigrants from Poland. They came to America at a time when people were looking for the economic and religious freedom of 'the American dream'.
Miller's father ran his own tailor's business and the family were very well off. In the 1920s there was a massive financial crisis in America, which is often referred to as the Wall Street Crash (Wall Street was where the New York financial and banking centre was located). The Miller family was ruined and the impact of the loss on Miller's parents, especially his father, made a big impression on the young Arthur. He saw it as a failure of the American dream and of the economic system (known as capitalism) on which his family had built their hopes of a better life.