William Carlos Williams had an entirely parallel career as a doctor in his hometown of Rutherford, New Jersey. This work allowed him to write his poetry unencumbered by financial concerns. It also gave him unique insight into people's everyday lives. He often remarked that his work was an integral part of his literary education as it grounded him in the reality of his patients.
Williams studied medicine at the University of Pennsylvania. Following this, he completed his internships at two prominent New York hospitals and traveled to Leipzig for additional coursework in pediatrics. Williams settled into private practice and worked for forty years as a physician in Rutherford. Williams's friends and family claimed that he took great pleasure from his work and believed in its inherent value to the literary half of his life. In observing births, deaths, and the many struggles endured by the people he cared for, Williams felt that he came closer to a more complete understanding of the human condition. He often wrote poems on scraps of paper lying around his office. He didn't attempt to sharply separate these two careers; there was significant overlap between his medical profession and his literary one. One can further speculate that his attempt, in his poetry, to communicate as clearly and simply as possible was related to his close view of the everyday battles of his patients. In seeing the world more concretely, he was motivated to seek out a form that would capture these difficulties with artistic honesty.
Given this context, it seems fitting that he chose to set "Between Walls" at a hospital. This is especially true given that it is a poem that seeks to find beauty in the forgotten back area of this place. While the poem does not seem overtly biographical, it follows that Williams would try to find beauty in such a place, as he likely was often trying to find the same glimmers of grace in his own daily medical practice.