A "crucible" is a severe test or trial, which is exactly what happens in the play. Miller intended "The Crucible" as an allegory to McCarthyism. The events that took place during the time the play was written were very similar to the Salem witch hunts. Innocent people were being put on trial or jailed practicing or being associated with what people believed to be evil- communism. Miller himself was accused of being a communist sympathizer. Like the people put on trial during the witch hunts, McCarthyism accused also had their reputations damaged or even their lives ruined.
According to the Miriam Webster dictionary there are three definitions of crucible.
1 : a vessel of a very refractory material (as porcelain) used for melting and calcining a substance that requires a high degree of heat 2 : a severe test 3 : a place or situation in which concentrated forces interact to cause or influence change or development
Arthur Miller could have been referring to either one of these definitions.
The vessel could be a symbol of the people, courts, and town heated with fear and greed. This creates a change of emotions and feelings that effect their actions.
The test may represent a test of the people's beliefs, morals, and values.
The last definiton seems to fit most appropriately. The concentrated forces (people, courts, town) interact to cause change. The change ultimately would result in less religion in courts as well as less acceptance of hearsay