An air mattress provides a "storable" bed. It can be deflated when not needed and put away. When needed for guests or other reasons, it is inflated. Many air mattresses have pumps, sometimes battery operated or configured to get power from a car in order to make them easier to inflate on camping trips.
A benefit of an air mattress is that it can be adjusted to different levels of firmness. For that reason some regular mattresses and folding sleeper bed couches have an air mattress layered on top of a regular mattress.