How does the title of Arthur Miller's The Crucible highlight key ideas explored in the play?

It's probably best to explain what a crucible is before finding quotes. In science, a crucible is a container that will hold materials that are likely to be subjected to extremely high temperatures. The things inside the crucible change by being melted or even destroyed, yet the crucible remains in tact. Things are tested inside of a crucible, and that is how the title is well applied to this play. The town of Salem could be the crucible that holds the people that are being tested, or the witch trials themselves are the heat that is being applied to the situation. The people that withstand the heat are the people that are crucibles. Either interpretation is able to be defended.
I would say the best character to illustrate the idea of standing firm and withstanding the outside pressures of the witch trials is John Proctor, Giles Corey, or Rebecca Nurse. Granted, those three are not the only three people accused of witchcraft that refused to confess and were killed because of it, but the play does a nice job of highlighting their strength. The Puritan beliefs in witchcraft were very real, and the accused were between a metaphorical rock and hard place. They could deny the accusations and hang, or they could confess the lie, live with damaged reputations, and a belief that they were going to hell for telling that lie.

PROCTOR, sensing her weakening: Mary, God damns all liars!DANFORTH, pounding it into her: You have seen the Devil, you have made compact with Lucifer, have you not?PROCTOR: God damns liars, Mary!

Toward the end of the play, John is seriously considering the lie in order to save his life and stay with his wife and kids; however, after seeing that Rebecca Nurse was holding firm, he can't go through with signing his name to the confession.

DANFORTH: Then explain to me, Mr. Proctor, why you will not let—PROCTOR, with a cry of his whole soul: Because it is my name! Because I cannot have another in my life! Because I lie and sign myself to lies! Because I am not worth the dust on the feet of them that hang! How may I live without my name? I have given you my soul; leave me my name!DANFORTH, pointing at the confession in Proctor's hand: Is that document a lie? If it is a lie I will not accept it! What say you? I will not deal in lies, Mister! (Proctor is motionless.) You will give me your honest confession in my hand, or I cannot keep you from the rope. Proctor does not reply. Which way do you go, Mister?His breast heaving, his eyes staring, Proctor tears the paper and crumples it.

Hale and Parris beg Elizabeth to go to John and convince him to change his mind, but Elizabeth knows how important it is for John to stand firm. He's being tested, and he is coming through it with a pure and good heart.
Hale: Woman, plead with him! He starts to rush out the door, and then goes back to her. Woman! It is pride, it is vanity. She avoids his eyes, and moves to the window. He drops to his knees. Be his helper! - What profit him to bleed? Shall the dust praise him? Shall the worms declare his truth? Go to him, take his shame away! Elizabeth, supporting herself against collapse, grips the bars, of the window, and with a cry: He have his goodness now. God forbid I take it from him!