The term "crucible" also means a "severe test or trial", according to dictionary.com. The characters in the play all experience a severe test or trial beyond the obvious witch trials. Elizabeth's honesty and, thus, goodness is tested during the trials when she is asked why she fired Abigial. John's fidelity to his wife is tested by Abigail, and thus his goodness too throughout the course of the play. Parris' reputation is on trial when witchcraft is found to be occurring at his home. Mary Warren's honesty is tested, as is her courage to do the right thing, when Abigail accuses her.
"Crucible" is defined as a vessel for melting substances together requiring extreme heat. This is exactly what the people accused of being witches go through...extreme heat and questioning giving what is perceived as inferior answers in the face of a stern court which is determined to "get to the bottom of this" and move on. The girls are good at acting their parts and seeing the "spirits" of the accused flying at them in menacing ways, and before you know it, many innocent and formerly respected members of the community of Salem are hanging or crushed and dead.
The "Crucible" is also the name given by US Marines to one of their obstacle courses during basic training. It is supposed to be a tough course that one can only succeed in mastering through determination, strength--both physical and mental, and perserverance. That sounds appropriate for this play as well.