Here's why this is important:
* The lack of a profession reinforces the narrator's confinement and dependence on her husband. The story takes place in a secluded country house where the narrator is isolated from any external activities or social engagements. This lack of a professional life contributes to her increasing sense of isolation and frustration.
* The "rest cure" itself is a critique of medical practices of the time. This "cure" was often prescribed for women suffering from "nervous disorders" and involved complete rest, isolation, and a lack of intellectual stimulation. The story suggests that these treatments were not only ineffective but also harmful, leading to the narrator's mental deterioration.
Although the narrator's exact profession is never revealed, we can infer from the details in the story that she had an active and intellectual life before the "rest cure." This makes her current state of confinement and inactivity even more frustrating and oppressive.