During inhalation, the diaphragm contracts. As it contracts, the diaphragm moves downward, increasing the volume within the thoracic cavity. Due to this increased volume in the thoracic cavity, a negative pressure gradient is generated which causes air to flow from the environment into the lungs. The lungs expand as the alveoli of the lungs fill with air.
During exhalation, the diaphragm relaxes and rises into the thoracic cavity, decreasing the volume in the thoracic cavity. The decreased volume in the thoracic cavity results in an increased pressure which causes air to flow from the lungs out to the environment. At the same time, the lungs are elastic and act to help air flow out as the retract after being expanded.