Proctor wants Mary Warren to speak on behalf of his wife at the trial proceedings and denounce Abigail. Proctor knows and Mary knows that all of the accusations are false, done in the name of preventing the night out in the woods that the girls had. At the end of Act II, Proctor is confronted with the reality of more people, such as his wife, being imprisoned. John understands that Mary is his only chance at stopping Abigail because it is someone from her inner circle that is speaking out against what she is doing. I think we see Proctor ask Mary Warren for her help at the conclusion of the act. It is a point where she continually sobs her objection and one where Proctor begins to show a level of intensity that had not been seen prior. It is a moment where Proctor is asking, but is more demanding that justice be done and that Mary Warren become the instrument that allows this to happen. At the end of Act II, it becomes evident that Proctor needs Mary Warren to help him defeat Abigail through the legalistic machine that is already in place in Salem. It is at the end of Act III where Proctor makes one more leap in his evolution regarding this configuration of institutional "justice."
Ultimately, John wants Mary Warren to speak in court with him to discredit Abigail Williams.
Earlier in Act II, Mary Warren came home from the court proceedings with a "poppet." She made the doll during the court proceedings, and she stuck her needle in it for safe keeping. Abigail watched Mary do this, and Abigail used the circumstance to cast suspicion on Elizabeth Proctor.
Hale: Abigail were stabbed tonight; a needle were found stuck into her belly -
Abigail is claiming to the court that the poppet belongs to Elizabeth and that Elizabeth somehow used the doll to force Abigail to stab herself with a needle. John wants Mary to go to the court and explain how the doll is hers and not Elizabeth's doll. John also wants Mary to explain that she placed the needle in the doll during the court proceedings.
Proctor, moving menacingly toward her: You will tell the court how that poppet come here and who stuck the needle in.
John hopes that this will be sufficient evidence to prove that Abigail is lying to the court. Unfortunately, Mary is terrified of what Abigail might do to her in return.
Mary Warren: She'll kill me for sayin' that!