The narrator of "The Yellow Wallpaper" is a woman trying to cope with involuntary thoughts and impulses caused by mental instability; she tries to manage these challenges by writing in her private journal, and the shortness of the paragraphs emphasizes the choppy and disjointed nature of the narrator's thought process. Here in the short paragraphs, the reader has literary proof of the narrator's pathologically busy brain, which is the most obvious element of the narrator's character.

As well, the narrator reveals her highly sensitive nature in her short paragraphs full of details describing her surroundings. In her writing, she admires the beauty of the garden, and she comments on the appearance of her room. Her sensitivity and her careful eye are evidence of her interests beyond the room in which she is living, interests like the outside world and aesthetic concerns like colors and the prettiness of other rooms in the house.

The short paragraphs in Charlotte Perkins Gilman's story, "The Yellow Wallpaper," are important to understand the narrator's state of mind. When paragraphs are shortened and sentences repeat themselves, this reveals the narrators madness or mania escalating. She can't express extended thoughts and what she says is hardly coherent. Gilman uses language to reflect what is occurring in the narrator's mind. 

Though the narrator is writing or telling what she is feeling in a journal--which she must sneak from her husband--she has difficulty making sense as the story goes on and she becomes less grounded in reality. Authors often use narrative structure to reveal character development. In this case, the short paragraphs and choppy sentences show the narrator's mental decline as the effects of isolation and rest on a person who is suffering from postpartum depression.