An airbase is a military home for aircraft. Planes take off and land there, and the people who fly them and fix them live and work there too. It is more than a strip of runway: there are hangars, fuel, often weapons, and somewhere for the air-force people to sleep. You will hear it in the news ('stationed at an airbase') and in military talk. It is also written as two words, air base; that is the same place. A civilian airport is not an airbase, even if a military plane sometimes uses it. The word is formal-to-neutral, not slang.