Numerous suggestions are always made regarding an author's choice of title (if the author fails to provide his or her reasoning). In the case of Arthur Miller's The Crucible, the title's significance lies in the definition of what a crucible is.
The first meaning found in the dictionary is as follows:
"a ceramic or metal container in which metals or other substances may be melted or subjected to very high temperatures."
In this case, one could look at the crucible as a metaphor for the village of Salem. The villagers put "heat" upon one another until they begin to "melt" (metaphorically) under the pressure. The accused villagers then either bend and break (as does heated metal) under the pressure put on them by the courts to confess to witchcraft.
The second definition is far more apparent:
"a difficult test or challenge."
In this case, numerous villagers must face a crucible. John must face his adultery. Giles must face the fact his accusations about his wife reading led to her being charged with witchcraft. Elizabeth must face the challenge of forgiving John. Parris must face the faction created against him. Numerous villagers must face a difficult test.