I think that Proctor's crucible is becoming an involved person in a time or crisis. When Proctor is first introduced in Act I and the start of Act II, he is one who does not want to get involved. He recognizes that there is madness around Salem, but he would rather disengage himself. His crucible is to what extent and how long can he remain silent. Slowly, his character begins to change in that he recognizes that his remaining silent actually emboldens those in the position of power that wish to continue what is happening. The battle for what will later be termed as "his name" is what ends up driving him throughout the drama. It is his crucible to actually stand for something in a world where few stand for anything. The intense pressure and emotional "heat" by which this comes about is a crucible for Proctor. It is not easy. It is not pleasurable. Yet, it is a reality that he must endure or face as the drama progresses. It becomes a crucible for him because it forces him to test his previous resolve of disengagement or not wanting to involve himself with what is happening. Slowly, Proctor ends up emerging through this crucible as a man with "goodness," as Elizabeth notes, and as someone who will not have this "taken" from him.
The 'severe test' that John Proctor is put through is that concerning honesty.
He is forced one of two things; he can either be completely honest, yet lose his 'name' or reputation to all. Or, he could lie, keep his reputation yet be more likely to lose his wife who is suspected to be a witch.
By finally choosing to be honest to society, John Proctor shows his audience that he is willing to do all it takes to save his wife; therefore he shows that he is remorseful for the things he had committed to in the past (being the affair he had with Abigail). He shows that he places his wife at a higher level than his own being. The audience can distinctly interpret John's guilt in this sense.
However, even when John Proctor spills the beans concerning his wrong doings, he is still not able to achieve the desired result. Still the judges believe the young girls, and this acts as a synecdoche which highlights the unjust/biased society in which John Proctor lives.