Sidechaining takes one sound and uses it to manipulate another sound. Most often you will see it on compressors, gates, limiters, and expanders. However, it can also be found on vocoders, synthesizers, and other effects. It is a really, really useful feature on compressors and gates because it allows you to place multiple instruments in the same frequency range without clashing.
Ducking describes what happens when you over compress or limit a sound but with a sidechaining compressor this is the effect created. Ducking is the technique used by french house producers to get their characteristic “pumping” sound. Here are two snippets from popular french house songs that make heavy use of ducking (sidechaining):
Listen to the horns in the Daft Punk sample. Notice how they become quiet when the kick drum plays? That’s ducking. The horn volume is ducked to make room for the kick drum. Listen to the DJ Falcon sample. The vocal loop gets ducked for the kick drum in the exact same way.