The word "crucible" may be defined as being "a severe test, as of patience or belief; a trial." A secondary definition is "a place, time or situation characterized by the confluence of powerful intellectual, social, economic, or political forces."
The Crucible tells the story of the Salem witchcraft trials, a period in American history in which women who did not conform to the expectations and patterns of accepted behavior for women in that location and time were persecuted and executed on the basis of minimal evidence backed by substantial gossip and fear. For the women victims, the play certainly was "a severe test or trial." Salem showed itself to be a location and situation in which deeply-held beliefs regarding religion, faith, sexuality, and morality came together in a powerful collision.
The title of Arthur Miller's play, The Crucible, may be interpreted in several ways.
Firstly, we have the literal meaning of the title. A crucible is a place or situation in which people or ideas are tested, often creating something new in the process (which is basically what happens in the play)
And secondly, we might interpret the title in a more metaphorical way, stating that a crucible is also a metal container used for melting sustances and as a result, something flows up and it is purified. This metal container is used as part of a process which's aim is to remove something impure.
Though this last definition (most often than not) refers to chemical processes, you might be able to argue that it can also be applied to the play's theme.
Hope it helps.