How does this quote display a metaphor "I will not have it said my name is soiled" and what is the significance?
Abigail [in a temper]: My name is good in the village! I will not have it said my name is soiled! Goody Proctor is a gossiping liar! (Act I, pg 21)
The quote is fairly significant in that it reflects the twisted nature of individual reputation. Abigail's proclamation of having a good name and reputation is belied by her actions. Her affair with John Proctor, her construction of lies about witches and those who are practicing witchcraft, as well as the desire to usurp Elizabeth's role are all examples of her motivation despite professing to having a "good reputation." Her use of the term "soiled" is powerful because while she seeks to not have her name slandered, she does this to nearly everyone else that stands in her path. She seeks to be clear of the dirt and mire of slanderous accusations, yet embroils others in the same filth. The metaphor invoked here reflects someone that is able to speak of pristine reputations, while targeting others'.
If you are going to call this a metaphor, the metaphor exists between Abigail's name, and soil.
Often a metaphor compares one grammatical form to another grammatical form. Here you have her name, a noun, and then the comparison position word is 'soiled', an adjective. Grammatically speaking, this is a predicate adjective, not a metaphor.
But let's say you're going to use it as a metaphor. Abby's name represents her reputation, and it is compared to dirt, soil. She fears this especially because she lives in the Rev. Parris' home. She should have a good reputation.
The significance of this quote is that Abigail is angry because Elizabeth Proctor has said that she (Abigail) was having an affair with John Proctor, Elizabeth's husband. This is very important to the story because this affair (you can argue) causes both Elizabeth and John Proctor to be convicted of witchcraft on Abby's evidence.
I personally would not call this metaphor. I guess you can say that it is metaphor to say that a name is dirty, but I'd call it personification, myself. I say this because her name is not being compared to anything in particular. I think it is being treated as a physical thing (it can get dirty) and that is, to me, personification.