In relationship to "The Crucible", what did Senator Joseph McCarthy have to do with the Red Scare of the 1950s?
The "Red Scare" of the 1950s referred to an attitude experienced during the Cold War. The Cold War was a time period of open hostility between the US and the USSR. There was no actual violence in this war, but there was always the threat of violence. The situation fueling the hostility was the differences in government - the US was firmly in favor of democratic government, the USSR in favor of socialist government.
The "Reds" referred to the socialists, commonly known as the communists. The scare covered a number of fears - the spreading of socialism and pushing aside of both democracy and Christianity; and the threat of nuclear attack from the Russians.
Senator McCarthy led a number of senate hearings geared towards exposing traitorous factions in our own government and society. He wanted to expose anyone sympathetic with the socialist/communist movement and put those individuals on trial for treason. What ended up happening, however, was a hysterical witch hunt, involving many allegations and little real proof. McCarthy got so wrapped up in the "Red Scare" that he lost sight of real dangers.
These trials are what inspired Arthur Miller to write The Crucible. He drew the parallel between McCarthy's hearings and the Salem Witch Trials and wished to point out those parallels to the public at large.
McCarthy led the accusations that swept through hollywood and gave rise to mass hysteria, fearing communist infiltration in films, tv shows, commercials, etc. This fear of communist infiltration was known as the Red Scare. Those accused included Arthur Miller (who wrote a play, The Crucible, as a commentary on what was happening at that time), Walt Disney, and Lucille Ball. McCarthy's accusations led to the accused having to go before the HUAC (House of Unamerican Activities Committee) and either confess and provide the names of other communists, or not confess and risk imprisonment, fines, blacklisting (meaning you could not be employed in any aspect of show business), etc. There was no way to deny an accusation and the only way to go free was to provide names, which many did including Walt Disney. Hundreds of actors, producers, directors, writers, etc., were accused, many of which lost their careers and/or suffered irreparable damage to their lives.