How is a crucible tied in with The Crucible?
Another way to ask this question is, "What is the meaning of the title of The Crucible?"
There are at least two ways the title is intended to be understood. First, there are connotations of witchcraft attached the term crucible.
...a crucible is also a witches' cauldron in which ingredients are brewed together to be used in black magic.
The connections between this notion and the action of the play is clear.
Also, a crucible is an implement used to heat and reduce and concentrate a substance.
The story of the play features extreme circumstances where characters in a small and confined community are forced to decide and to prove their fundamental qualities. The characters undergo pressures that force them to confess, to display and to discover their true natures. This is true in particular for Hale, Elizabeth, Proctor and Danforth.
For instance, the pressures on John Proctor force him to publically confess a crime that he would very much prefer to keep private. However, he must confess to save the life of his wife. He is reduced by the circumstances of the play, forced by the situation to publicly define himself as an immoral person.