What is the significance of the title The Crucible as it relates to the major characters and theocracy?

A crucible is a bowl in which substances are ground and then purified.  As the term is used in the title of this play, "crucible" represents both a test and a purification process.  The major characters are placed in situations that try their characters.  According to the laws at that time, anyone accused of witchcraft was brought before the courts to testify. Answering "no" to a charge of witchcraft could result in death at the gallows, since the jury generally ruled that the person was, in fact, a witch.  Answering "yes" led to imprisonment, so that the accused could await sentencing.  In either case, all real property was lost; the state confiscated it.  

John Proctor, Goody Nurse, and Giles Corey are tested by the courts, and all go to their deaths.  Despite their pleas of innocence, both Proctor and Nurse are hanged.  Giles Corey refuses to plead, for he knows that he will lose his property either way.  As a result of his stubbornness, he is pressed to death.  

The theocratic government of the colony ruled absolutely in all trials related to suspected witchcraft.  Residents were bound to abide by the rules of the church leaders. To ignore the rules of the church was to place oneself in a dangerous position.  In that way, then, the church leaders placed their church members in a perpetual test.  The witch trials purified the community by diminishing the degree of control the theocrats held over it.