A crucible can be defined as a test and a metal or ceramic container in which chemicals are combined at high temperatures. In "The Crucible," Salem's morality and logic are tested. Although there are some ethical and logical characters (i.e. Elizabeth Proctor and Giles Corey), Salem largely fails this test, allowing themselves to be herded by the religious fanatics and power-hungry citizens and officials to the point of widespread hysteria, and this hysteria is analogous to the high temperatures and potentially violent interactions of chemicals in a crucible.
One of the main messages of "The Crucible" is that mob mentality in any situation, religious or political, leads to thoughtless (and therefore unethical and illogical) actions. In this play, those actions lead to the persecution of innocent people. Although Hale comes in to asses the situation, when he begins to see that these accusations have no merit, he is vetoed by Danforth who would rather see innocent people executed than see the court's authority questioned.
Another message is that any society governed by oppressive laws and religious doctrines tends to lead to fanatical ideology. And under such repressive governance, some citizens will rebel; and in some cases, a rebellion is justified.
There are quite a few messages in the play and they all intertwine. One of the more basic statements the play makes is that religious doctrine is only ethical if it can be applied in a moral and logical way. These accusations of witchcraft, from a legal or religious standpoint, are neither ethical or logical. Legal and religious doctrines must pass the "test" of being applied in real life while retaining moral and logical justifications. Such doctrines should not be manipulated to persecute innocent people. And in "The Crucible" the accusations were upheld so the religious leaders and court officials would not lose any respect or authority. That is, the court (Danforth) upheld the accusations of witchcraft despite evidence to the contrary; he did this so the court officials and religious leaders would not have to admit their mistake.