Dynamic saturation exaggeration What is this type of processing called?

In some popular songs with a very strong bass beat, the strength of the bass beat is exaggerated by momentarily "turning down" the rest of the sounds while the bass beat hits.
Yup, don't know why datageist didn't expand, but it's called ducking.  The song or part of it 'ducks' out of the way of a signal, usually a big ol' kick.

You can insert a compressor into the signal chain of the track to be ducked, with a side-chain key input (as J.K says): meaning that the kick's amplitude/level will cause the mix to be compressed, i.e. reduced in volume.