Sidechain compression uses the signal from one track (the sidechain input) to trigger compression on a different track. The classic example: a podcast intro/outro music track is sidechained to the host's voice track — whenever the host speaks, the music automatically ducks down in volume, then rises back when they stop. The same technique is used in electronic music to create the 'pumping' effect (kick drum sidechained to a synth pad).
Most DAWs support sidechain compression natively. In the compressor plugin, you select an external sidechain source (the voice track, the kick drum) and the compressor reacts to that source's level. This happens in real-time and is fully automatable. It eliminates the need to manually ride volume faders for ducking.
Sidechain compression is distinct from sidechain filtering, where you filter the sidechain input (e.g., high-pass the kick drum so only the transient triggers compression, not the sub-bass sustain). Both techniques are fundamental to modern mixing.