sidechaining is when the compressor works indipendantly to the sound its compressing?
Not exactly, from what I understand...it's more a way of using the compressor's "smarts" to trigger some other effect as well. Compressors are "smart" because they listen to the incoming audio and choose when they should do their thing, based on the threshold setting. A sidechain lets you send that "effect ON" command that the compressor sends to itself to another effect as well.

So you can be compressing one track quite happily, but rigging up a sidechain from that compressor to another effect lets you say "oh, yeah, and whenever that compressor gets triggered, I also want you to trigger a ducker effect on the bass on this other track." So your compressor is also controlling other effects, and the sidechain makes sure that the other effect gets triggered when the compressor does.

In theory, you could hook a compressor sidechain up to reverb (or whatever), such that something gets reverb whenever compression kicks in, but there wouldn't be much point to that...a ducker, gate, or another compressor seem to be the most useful things to sidechain to (I've heard of sidechaining a compressor up to a gate on the high hats, for instance).