The beginning of Act 2 establishes the cold relationship between John and Elizabeth. The affair he had with Abigail is known only between them. John wants to keep it that way (as I'm sure Elizabeth doesn't want anyone else knowing in town about it either.) Elizabeth encourages John to go to the court and explain to the men of council what Abigail's reasons really are for this "witch" talk. He knows she's just pretending and has found power in such talk. However, when Abigail admitted that it was only pretend, he was alone with her. It will be his word against hers. He is afraid that talk of their affair will come out and be used against his name/family. He also knows that the affair will eventually come out, and his main internal struggle throughout the play is knowing he can't escape his past, and yet he wants desperately to stay out of it.
Miller includes these details to set up what later happens when John refuses to admit his guilt to the court. In the end he loses his life, but his actions restore his soul. That was his struggle all along.