Compressor in the sidechain is more commonly heard during voiceovers where music automatically dies down when the announcer starts to talk. In music, sidechaining the compressor is more commonly heard when you want to 'sync' the bass with the kick - a common technique used in dance music.
What is done is that the compressor is inserted into the track that will be compressed and it's sidechain input is fed a signal from the track that will trigger the compressor. In dance music, often the bass track is compressed with the sidechain fed from the kick. Set a fast attack, and by manipulating the release and threshold parameters, you can get the bass to sound in time with the kick.
