A sidechain feeds a processor a different signal to listen to than the one it affects. The classic use: a compressor on the bass listens to the kick, so every kick pushes the bass down and the mix breathes in rhythm. House and EDM turned that pumping into an aesthetic signature.
The pattern generalizes: any detector controlling any parameter, keyed by any source. Ducking under a voiceover is a sidechain; so is a gate opening hi-hats only when the snare fires.
Audio-reactive visuals are sidechaining by another name: sound in the detector, image in the processor. The kick ducking a bassline and the kick slamming a visual are the same circuit with different outputs.