The diaphragm is a large, dome-shaped muscle that separates the chest cavity from the abdominal cavity. When you inhale, the diaphragm contracts and moves down, creating a negative pressure in the chest cavity that draws air into the lungs. When you exhale, the diaphragm relaxes and moves up, pushing air out of the lungs.
The diaphragm is also responsible for supporting the spine and abdominal organs, and for helping to maintain balance. In saxophone playing, the diaphragm is used to control the airflow through the instrument, which is essential for producing a clear, consistent sound. A strong diaphragm can also help to prevent fatigue and injury.