At the beginning of Act IV, the authorities are somewhat worried. They are going to be hanging John Proctor and Rebecca Nurse the next day. This worries them because these are the first of the people to be executed who are really important and well-thought of in the community.
Because they are respected, it would be really good for Danforth and Hathorne if Proctor would confess. Then people could not be angry at the two of them for hanging an innocent man.
But Proctor will not confess, or at least he won't sign the confession and ends up tearing it up. What he gains is self-respect and his good name.