The overall conflict in The Crucible is witchcraft. Salem is worried about the future of their town and haunted by the idea of witched living among them. Abigail Williams uses this fear of witchcraft to her advantage and is dishonest with the officials of the court.
One character that contributed to the conflict of the story is Abigail Williams. She is very manipulative and blackmails people. She is the one who made up the story of witchcraft and lies to convince the court on who the witches of Salem are.
I never knew what pretense Salem was, I never knew what lying lessons I was taught by all these Christian women and their covenanted men!"
One major complication was when Elizabeth Proctor was jailed by Abigail Williams. In this part of the story, she is framed by Abigail to have a poppet, sent by Mary, put in her house with a needle in it. Mary Ann says "She will kill me and charge lechery." In this, you can see how manipulative Abigail really is.
The conflict has not really been solved although the idea of witchcraft is being questioned by the court officials.