Expiration takes place when the intra-pulmonary pressure is higher than the atmospheric pressure. The diaphragm and a specialised set of muscles-external and internal intercostals between the ribs, help in generation of such gradients.
Relaxation of the diaphragm and the intercostal muscles returns the diaphragm and sternum to their normal positions after inspiration which reduces the thoracic volume and thereby the pulmonary volume. This leads to an increase in intra-pulmonary pressure to slightly above the atmospheric pressure causing the expulsion of air from the lungs, i.e. expiration.