As the story progresses, the woman in the wallpaper increasingly represents the narrator's deteriorating mind, and is a symbol of her own feeling of being trapped and imprisoned by her family and circumstances.
Notice at the beginning of the story she does not see a woman in wallpaper; rather, she focus on its ugliness, on how it is "an artistic sin." But as she is forced to spend more time in the horrid room, alone, separated from her work, from socializing, from seeing her son, and from doing anything productive or active, she begins to see a woman in the wallpaper. At first, it isn't even a clear form:
"But in the places where it isn't faded and where the sun is just so I can see a strange, provoking, formless sort of figure, that seems to skulk about behind that silly and conspicuous front design."
She feels that behind the main design of the paper, there is a figure lurking. Eventually, that figure becomes a woman, then a woman behind bars, then a woman longing to get out of the bars, then multiple women crawling around. At the end of the story, she herself has become that woman, crawling around and around the room trying to thwart her imprisoners. So the woman in the paper represents her, and her feelings of imprisonment, confusion and captivity--it's a symbolic representation of her powerless state, both mentally and physically.
I hope that those thoughts helped; good luck!