An automatic mixer controls a group of live microphones, turning up mikes where someone is talking, and turning down mikes that aren't being used. This is a real-time voice-activated process, completely different from studio automation that only plays back pre-recorded moves. People have tried to do automatic mixing with gates, but experience has shown that in most live situations it isn't possible to find a gate threshold that will work without obvious chopping. This is because sometimes, when the room is noisy, the noise level at the microphone is higher than the voice level will be at another time when the room is quiet. An automatic mixer can adapt to changing conditions, whereas a gate can't.
Another problem that automatic mixers must solve is the additive effect of multiple mikes being on at the same time. If one mike is on at maximum gain, opening up another one will make the system feed back. So an automatic mixer must also keep track of the gain of the whole system to prevent feedback or excessive noise pickup.
A final problem that automatic mixers should solve is maintaining a natural ambience from the room. This is especially critical in recording and broadcasting. A good automatic mixer should be able to make rapid and dramatic changes in the gains of the input channels while maintaining the sonic illusion that nothing is happening at all.
It's important to understand that automatic mixing is not limiting, not compressing, and not automatic gain control (AGC). Automatic mixers may incorporate these functions, but the term automatic mixing per se means controlling multiple mikes so that the system gain goes where it's needed.