The narrator's evolving relationship with the wallpaper in her bedroom demonstrates her mental breakdown, and her inability to recognize her deteriorating mental health helps readers to recognize her as fundamentally unreliable. To be clear, she does provide a reliable narration of her own experiences as she experiences them, but we cannot rely on her to provide objective or accurate information about much else.
At first, she simply hates the wallpaper, and she feels that it could be "one reason [she does] not get well faster." She analyzes the paper, saying that it commits "every artistic sin" and that its lines "commit suicide": extreme and troubling remarks, but they also provide evidence of her education and intellect and imagination. Soon, however, she says,
This paper looks to me as if it knew what a vicious influence it had!
Now she is ascribing consciousness and intention to the wallpaper, suggesting that it is actually aware of its effect on her and is, perhaps, purposely attempting to produce this effect. It does not take long for her to decide that she might be improving "because of the wallpaper." Without stimulation, and absolutely beset with boredom, the narrator has nothing to think about but the wallpaper, and she begins to feel that there are two patterns in the paper. She admits to lying awake "for hours trying to decide whether that front pattern and the back pattern really did move together or separately." She comes to see life as "very much more exciting now that it used to be" because she has "something more to expect, to look forward to, to watch": she means the wallpaper.
It is not a sign of good mental health to look forward to one's life so that one can study the life of one's wallpaper. The narrator does not realize that this is not really a positive mental development. She's becoming obsessed with the paper, with keeping her sister-in-law from understanding it; she even grows possessive of it. The narrator develops the idea that there is a woman behind the first pattern of the wallpaper and that "[this woman] just takes hold of the bars [in the front pattern] and shakes them hard." Obviously, we know that the wallpaper is not alive, that there is no woman trapped within it, and we can understand that the narrator's descriptions of this inanimate object signal her declining mental state, though she does not realize this. This helps us to realize that she is no longer reliable as a narrator.