How is "The Crucible" a proper title for the play and what characters emulate it?
One definition for "crucible" is a severe test or trial. This is the definition most often attributed to the play. There is a direction connection: within the play, the witch trials were very severe. Also, many characters underwent severe trials, specifically John Proctor, who not only was put on literal trial, but his integrity, morals, honesty, and convictions were tested.
Other definitions refer to a container where metals are melted down and fused; the high heats melt most metals, but not all. In this definition, we can see that many characters (Mary Warren, Goody Good and Osburne) "melted" under the severe heat and pressure of the witchcraft accusation. But not John Proctor. He was made of tougher metal. He signs a confession at first, but in the end "tears the paper and crumples it" and then says, "You have made your magic now, for now I do think I see some shred of goodness in John Proctor". Being under the severe heat and pressure of this trial, the "magic" he refers to, he is transformed into a stronger man who has withstood what so many others were not able to.
The term has a few allusions in throughout the play. Danforth states, "We burn a hot fire here. We melt down all concealment." The image of fire associated with a crucible also underscores the concept of "The Devil coming to Salem" and the distress the trials and the events around the trials have caused in the community. Finally, although it didn't occur within the play or the actual historical events in Massachusetts, witches were set fire to and burnt at the stake.