Dynamic saturation exaggeration
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.