This explains it.
I use it for 2 things mainly,
Drums. I have 1 buss L+R of the drum mix going to Stereo with no compression at all (although some of the channels may have some compression beforehand i.e. snare and kick), a second L+R buss of the drum mix is going through a compressor and then to the stereo buss. By mixing the 2 you can achieve a punchy drum sound without it sounding squashed.
Vocals. I split the vocal recording to 2 channels of the mixer. I have 1 vocal channel running straight to the stereo buss with the normal eq, etc. The second vocal channel has a compressor inserted, this is compressed slightly harder (steeper ratio) than you would normally trying to act on the loud parts mostly, the compressed channel is then eq ed and I usually have the effects send going from this channel but not always depending on what I am looking for. By mixing the 2 vocal channels so that the uncompressed channel and the compressed channel are similar volume in the quiet parts and the compressed channel stays down in the loud bits with the uncompressed channel getting louder the vocal mix sits in the mix without it sounding over compressed. You have to experiment to get it right.
And sometimes I don't use parallel compression at all.
Alan.