Describe how Miller uses the symbol of fire throughout the play and explain what it represents.

In act one, the Reverend Parris confronts his niece, Abigail, about the girls' activities in the forest the night before. He says,

I saw Tituba waving her arms over the fire when I came on you . . . She were swaying like a dumb beast over that fire!

The girls were, evidently, trying to conjure the dead, and Abigail even drank a blood charm to kill Goody Proctor. The fire, here, seems to symbolize the girls' lawlessness and wickedness. Tituba never meant harm, but Abigail certainly did.
Mrs. Putnam also declares that "There are wheels within wheels in this village, and fires within fires!" Rebecca Nurse says that she cannot understand or explain why Mrs. Putnam has lost so many children, and Mrs. Putnam gets angry because she believes that a witch is behind her children's deaths. The "fire" in her quotation, then, figuratively refers to the evil and wicked conspiracy of witches that she feels is behind her tragedies.
In act thee, Deputy Governor Danforth tells John Proctor, "We burn a hot fire here; it melts down all concealment." He is referring to the court, where he claims to be searching out and upholding truth. In reality, the court is championing the lies told by deceptive children and killing innocent people in the process. The "fires" here seem to signify the court's corruption. At the end of the act, while Proctor is being arrested on the word of Mary Warren, he "laughs insanely," saying, "A fire, a fire is burning! . . . God damns our kind especially, and we will burn, we will burn together!" Proctor now sees that everyone that has, in any way, contributed to this corruption will figuratively burn—himself included.