What is the significance of the woman behind the yellow wallpaper and what does the woman mean to the story and to the narrator?
The woman behind the wallpaper is an extension of the narrator's personality. She is the freedom that the narrator is denied. The fact that the woman behind the wallpaper is able to move around at will and escape out a window into the landscape beyond is the narrator's dream. However, on the other hand, the woman behind the wallpaper is also imprisoned (crawling around and around desperately attempting to escape) as the narrator is--both in the room and in her mind since she (the narrator) is denied any outlet such as her journal or diary.
I might also add, the ugliness with which the wallpaper is described could be compared to the ugliness of her situation. She is being oppressed by the men in her life and by her inability to break the chains of their dominance in order to escape.