The reader is getting to fully experience the narrator's emotions first-hand.
Explanation:
The Yellow Wall-paper is a story that is composed of the narrator's diary entries. In doing so, the reader gets a first person point-of-view of how the woman is feeling about the house, her husband, the wallpaper, etc.
This was done to give the reader a very clear idea of how she felt. The story overall was intended to show the woman's spiral into madness, so writing it in a first person POV fully allows the reader to understand her thoughts and feelings. Had the story been written in third person, for example, the reader would not have been able to completely understand the woman's actions and behavior.
