Atmosphere is the general name for a layer of gases that may surround a material body of sufficient mass. The gases are attracted by the gravity of the body, and held fast if gravity is sufficient and the atmosphere's temperature is low. Some planets consist mainly of various gases, and thus have very deep atmospheres.
From an Orbiter pilot's point of view, an atmosphere is the nasty sticky bit around a sufficiently large planet; there are basically three sorts:
- Thin enough to give little aerodynamic benefit, but thick enough that you can't just ignore it. Example: Mars
- Thick enough to be useful aerodynamically; re-entry needs some care, but with sufficient preparation no fuel need be expended after the deorbit burn if a runway is available for landing. Example: Earth, Titan
A fuller description at Wikipedia: