It's called ducking, sidechain ducking, sidechain compression or sometimes even "sidechaining".
A compressor is a device which lowers the volume of a signal when it gets louder than a set threshold level. Compressors are used in many ways to alter the dynamics of individual instruments and mixes. In a sidechaining compressor, the "key" signal that's used to control the attenuator, is taken from a different place than the signal that's attenuated. For example, a string pad might be the processed signal, and a kick drum (bass drum) is used as the key signal. Every time the kick drum hits, the string pad's volume drops and rises back after a release time has passed.
A similar technique is used for example in radio shows, to automatically duck the background music when someone speaks to the microphone.
Sidechain ducking is used to glue sounds together and to let drums or other things be loud and pronounced all the time, while allowing everything else to be loud all the time too! :) Everything is loud all the time - win/win situation?
Another effect achieved with sidechain ducking that's used a lot in electronic dance music is rhythmic pumping. If the release time is set so that the ducked instrument comes back after a musical meaningful time value like 1/8 note after the kick drum, then the background pad pumps in sync with the kick drum beat almost as if it was a guitar or accordion playing a back beat. So, the compressor is used partly as an automatic mixer, or almost like an arrangement helper.
Here's a demonstration. The musical effect is the same, but kids these days don't want to hear accordions anymore, they want boom boom kicks and ducking pads. Same thing really. ;)