Imagine reading this on the wall while you wait for news about someone, or about yourself. The speaker starts with a small, practical warning about the doors: they swing both ways, and from either side the other side looks like "out." Patients and visitors, the sick and the well, each assume the exit is on the other side.
From there the poem turns to the body, which the speaker calls a mystery. A Klein bottle is a shape with no inside or outside, just one continuous surface. That is how the body feels here: you can't simply get into it and fix it. Even doctors' models are "flawed," so the body seems to cross itself, living "within the without."
The tone is calm, curious, and gently consoling. The wind-or-breath line suggests life can't be grasped or held. The ending offers a hopeful idea: sickness is a set of edges, and becoming whole means moving past them.