The sidechain is the circuit of the compressor that "sees" the material being worked on. Normally that would be whatever you feed the input of the compressor because that's what you want it to work on.
However, if you feed the sidechain something else, the compressor will think that this is the material that need leveling etc. It will then be completely blind to the material you're feeding the input.
So, you can feed the sidechain a heavily eq'ed version of the material to make it react to specific frequencies more than others. This way you will never hear the eq'ed version but the version you've fed the input will be compressed as if it were the eq'ed version. Makes sense?
Now, you can also feed the side chain something completely different. The classic is putting the compressor on the bass and feeding the kick drum to the sidechain. That way the bass will get compressed (ie the volume will get lower) every time the kick drum hits. This way you can avoid clashes as well as you make the kick drum seem more powerful (especially if you apply this technique on synths etc).
Another common way to use it is to compress the guitars whenever the vocals come in. Of course you always have to make sure the compressor is set appropriately in terms of threshold, ratio, attack etc. Experiment. Use those ears.