On a 1998 Camaro Z28, the term "air pump" usually refers to the
Air Injection Reactor (AIR) pump. This is part of the emission control system. It pumps air into the exhaust system during engine startup to help burn off unspent fuel and reduce emissions. It's also sometimes called the
secondary air injection pump.
It's a relatively simple device, driven by a belt from the engine and featuring a pump to force air. Failure of this system can lead to a check engine light and emissions test failure.