Abigail's power is based on several factors. First, she is a young, beautiful woman who uses her physical appearance to her advantage. She knows that the men in the town are attracted to her, and she uses this to her advantage to get them to do what she wants. For example, she convinces John Proctor to have an affair with her, and then she uses this affair to blackmail him into helping her cover up her role in the witch trials.
Second, Abigail is a skilled actress who can easily convince people of her sincerity and innocence. She is able to cry at will and make herself look terrified and vulnerable. This makes it easy for people to believe that she is telling the truth when she accuses others of witchcraft.
Third, Abigail is aided by the fact that the people of Salem are living in a time of great fear and paranoia. They are worried about the Native Americans who are living on the outskirts of their town, and they are also worried about the religious changes that are taking place in England. This makes them more susceptible to Abigail's claims, because they are eager to find someone to blame for their troubles.
Abigail Williams is a powerful figure in The Crucible because she is able to manipulate others and play on their fears and insecurities. She uses her physical appearance, her acting skills, and the prevailing climate of fear and paranoia to her advantage to get what she wants.