An omnidirectional microphone is a microphone designed to pick up sound from all directions.
The opposite of omnidirectional microphones would be unidirectional microphones which themselves are designed to pick up sound from only a single direction. No microphone is truly omnidirectional and no microphone is truly unidirectional, but some microphones come close to one or the other.
Omnidirectional microphones work by making sure that their transducer (the part that picks up sound and converts it into an electric signal) is exposed from all sides, which usually means that it is placed out of the "handle" in a "ball" or a "dome".
The benefits and drawbacks of omnidirectional microphones are obvious. They can be used to record more than one thing at a time, such as a whole band, but they also pick up a lot of other noise, such as room reverberations, audience noise, or even speaker feedback.