Gilman uses the description of the wallpaper to symbolize the havoc within the mind of a woman undergoing the rest cure. The narrator of the “The Yellow Wallpaper” perceives the wallpaper as a riddle that she must decipher. The narrator spends many days trying to interpret the “changing” patterns on the wallpaper. At first, the wallpaper is an “unclean yellow, strangely faded by the slow-turning sunlight” and “dull yet lurid orange in some places, a sickly sulphur tint in others.” With the passage of time, she sees the wallpaper start disintegrating and decaying, which symbolizes her own crumbling sanity. Her final mental breakdown is exhibited when, at the end of the story, she rips off the wallpaper, attempting to free the woman trapped inside: “The faint figure behind seemed to shake the pattern, just as if she wanted to get out.”
If you're talking about the one by Charlotte Perkins, the wallpaper symbolizes Family, Medicine, and tradition that the desperate woman feels trapped in, like a cage with metal bars.<span />