quite simply side chaining allows you to use a differnt source to trigger the compressor or a gate/expander

i.e. a compressor on a bass can be triggered by the bass drum so you get a musical reaction between the 2

simple really

It allows you to use something else to trigger the compressor. For instance, say you're doing a voiceover for a commercial. It has a music bed. To create what's known as a "Ducker" you would put the compressor on the music bed, and hook the vocal to the sidechain. Now, when the vocal kicks in, the compressor will drop the volume of the music bed. The threshold setting will correspond to the sidechain input, but everything else will affect the track the compressor is on.

Or you can put an EQ there, and have it affect those frequencies in particular, like say cut everything but 10 kHz to make a de-esser.