A crucible, in science, is an item that holds materials, like gold, for instance, over a flame in order to create a phase or chemical change. In the play, several of the characters are "held to the flame" and show who and what they really are. That is the connection to the other definition mentioned above--a difficult test or trial.
It is not just about the Witchcraft trials, however. John Proctor has to hold himself to the flame and come to terms with his indiscretion. He may have done wrong, but he refused to allow others to suffer for his sins. He is the man Arthur Miller wrote to represent himself- to examine his role in the events of his life and the Communist hearings in the 1950s.
it is! The word Crucible means test or trials of ones beliefs.