I liked the previous post's ideas of how the wallpaper is a reflection of self and a "manifestation" to quote post #2 of the woman's own condition. This idea in the story strikes a very powerful note of how we see our own selves mirrored in conditions that are separate from our own. In times of difficulty or sadness, we tend to see other things and people as mirroring our own predicament. In his work, The Book of Laughter and Forgetting, Kundera suggests that we do this, in part, to avoid being misanthropic, in that our scope of understanding and compassion widens when we ourselves are deprived of it. Certainly, the narrator is reflective of this. The story's demand for understanding the predicament of women and post- partum depression are both very strong, but its statement on the nature of mental illness and the demand to understand it, as opposed to merely covering it up in a "glib" (sorry, had to toss in a Tom Cruise dig there) manner by suggesting it to be a character weakness is the strongest of statements made in the story.
In one of his novels, Dean Kootz has a character remark, "Perception is reality." Such is the case with Gilman's character in "The Yellow Wallpaper." Because the wife/mother is confined to a room hideous to her with its cumbersome bed nailed to the floor and unsymmetrical, ugly wallpaper which is all she can contemplate, Gilman's character materializes her mental disturbances and repression into a woman imprisoned behind this wallpaper. In other words, her thoughts and feelings take a tangible form for her. Believing that there is this tangible form, Gilman's characters seeks to free her. Perhaps if her husband John can see this incarnate woman, he will then understand his wife's feelings. But, of course, he faints after coming into the room.
The woman in the wallpaper is a symbol of the narrator herself, and her increasing feeling of being trapped. She lives with a well-intentioned but overbearing husband who limits her options and pooh-poohs her suggestions like she is a child incapable of making decisions. Her brother is also a doctor who prescribes her unusual, and I feel, unhealthy cure of ostracization from society and limitations from working and staying busy and occupied. Because the narrator feels her voice in life is constantly being repressed, and every desire she has is not listened to or deemed foolish or unhealthy, she feels trapped. As her mental state worsens because of this repression, her ability to sense a woman in the wallpaper increases. She feels the woman is trapped, just as she is. She sees the woman trying to get out, just as she tries-and fails-to voice her desires and change her circumstances. In the end, the trapped woman in the paper just crawls around and around, trying to escape.
In the story, what starts out as the narrator just interpreting a crazy pattern on wallpaper becomes a full-blown manifestation of her repressed self; in the end, she and the woman in the wallpaper have become one and the same, and it is she that is skulking about the room along the edges of the wall.
The woman in that wallpaper is significant for the symbolic nature of a repressed woman's desire to be free and happy, and also of the narrator's deteriorating mental state as unfortunate circumstances are pressed on her. It is a sobering reminder of the situation that many women found themselves in during Gilman's time period, and an interesting commentary on the mind's ability to change its state for the better or worse.