What does the woman behind the wallpaper represent, and why does the narrator come to identify with her in "The Yellow Wallpaper"?
The woman behind the wallpaper represents the narrator's repressed self that she envisions as a prisoner in the domestic sphere of her life.
The more that the narrator looks at this wallpaper, the more a woman takes shape:
And it is like a woman stooping down and creeping about behind that pattern. I don't like it a bit. I wonder--I begin to think--I wish John would take me away from here!
This woman is the manifestation of the narrator's repression, her submission to the seduction of insanity represented by the yellow color of the wallpaper. As the narrator finds "things in that paper that nobody knows but me, or ever will," she perceives the faint figure of a woman "shake the pattern, just as if she wanted to get out." Eventually, the narrator becomes fixated upon the pattern of the wallpaper that changes with the light in the room and the figure that appears to be trapped behind the pattern.
Resolved to help this trapped figure, the narrator watches for her to begin to "crawl and shake the pattern," and soon, she pulls at the paper herself. Secretively, then, the narrator continues during the last day she is to occupy the room. As she does so, the narrator imagines more women outside who also are creeping, and she then believes she is the woman behind the wallpaper:
I suppose I shall have to get back behind the pattern when it comes night, and that is hard!
When the husband returns, he cannot open the door because the narrator has thrown the key outside onto the front path. When he finally gains entry into the room, he sees his wife creeping along the floor. "For God's sake what are you doing?" he demands. The narrator tells him,
"I've got out at last...in spite of you and Jane. And I've pulled off most of the paper, so you can't put me back!"
The narrator feels liberated from the forced confinement imposed upon her by John and Jane, a confinement that she has envisioned as a woman behind a hideous yellow wallpaper. Indeed, her repression of thought and action, her lonely confinement, and her sensory deprivation have all contributed to her terrible sense of repression from which she feels she must free herself.
The narrator sees the woman in the wallpaper as a prisoner, just like she is a prisoner in her room. She can't do anything that her husband and sister-in-law don't approve of, nor can the woman in the wallpaper escape.
While in the room, the narrator's depression becomes deeper and more advanced toward mental illness. Her desire to free the woman in the wallpaper is a cry from within trying to emerge from the psychosis that envelopes her. She can't seem to shake free of the melancholy that dominates her life.
"Despite her efforts, however, she cannot remove it all. In her desperation, she considers committing suicide but decides that this would be "improper and might be misconstrued." She begins circling the room, following the pattern of the wallpaper, in essence becoming the woman inside, trapped in an endless maze. John breaks open the door to see his wife creeping along the wall and faints. The narrator only laughs. His slumped body is blocking her path, and she is forced to creep over him each time she circles the room."