It is important to remember that this excellent short story is written in the first person point of view. Therefore, the person telling us this story is the unnamed woman who is struggling with depression, and therefore every description that we are given tells us a lot about her character. What is key to me is the way in which the narrator describes the yellow wallpaper in terms that clearly display her own mental instability at the beginning of the story. Consider the following description that we are given:
It is dull enough to confuse the eye in following, pronounced enough to constantly irritate and provoke study, and when you follow the lame uncertain curves for a little distance they suddenly commit suicide--plunge off at outrageous angles, destroy themselves in unheard-of contraditions.
Such descriptions of the lines in this pattern suddenly "committing suicide" clearly cast light on the narrator's character and her mental state. There is surely a parallel between the use of the adjectives "outrageous," "unheard-of" and "lame and uncertain," and the character of the narrator herself, especially when we consider the way that the narrator observes suicidal intent in the way that the lines "plunge off" and "destroy themselves."
This description therefore helps develop the character of the narrator by presenting us with her own mental instability, and suggesting her own despair through the detailed description that she gives us of the yellow wallpaper that oppresses her.