There are a few different elements of the setting that contributes to the story. The central symbol is the yellow wallpaper, I believe Gilman was trying to use the woman stuck in the wallpaper to symbolize the social position women played in society at the time. Gilman tries to show how women felt trapped and needed to "creep" when men were not looking. This also ran parallel to the narrator's life in the fact that the narrator felt trapped under he husband's care and felt the need to "creep" or write in her journal and other things behind her husbands back. .
The description of the house in the narrator's first entry foreshadowed that some terrible was to happen. How she always felt some thing strange about the house. And how there were some legal trouble with the heirs on the house. And how the greenhouses, which are known for growth and life, were all broken. The whole feeling and atmosphere for the room gave a questioning feeling to what part it"ll play in the story.
I also believe that the "great immovable bed" symbolizes the narrator's life. .
How she is married to her husband John and has no control in the relationship. .
The bed is old and worn and so is her relationship with her husband. And with both she cannot move or change either of them. She just wants to be free and in control of her own life not stuck in the same position in her marriage for the rest of her life.
The character of Jennie, I believe is the typical perfect woman for the time this story takes place in. She is content and willing to please. She is satisfied with her meaningless life and will do what is told. She is what the narrator feels she has to compete with. The narrator sees her as a perfect woman and wonders why she can't be like Jennie. .