Gibbous describes a certain phase of the moon, when it's bulging outward but isn't quite full. A waxing gibbous moon is one that's getting progressively rounder, night after night.
Occasionally the adjective gibbous is used for describing something else that protrudes or bulges, like a sleepy kitten's gibbous belly. Usually, though, it's used for the moon. When the moon isn't new (invisible from the earth) or full, it's either crescent or gibbous. Whenever the moon appears larger than a semicircle, but not quite a circle, you can describe it as gibbous.