Mid/Side, or the representation of stereo sound as the sum and difference of the two channels. What does that mean and why would we want that in a compressor?
The Mid/Side concept has its origin in stereo microphone techniques using two microphones (more about that here on Wikipedia ) but also gives us many options to change a stereo audio signal.
Now, if you can handle a bit of schoolboy algebra let's demonstrate how it works. To begin with, the 2-channel audio data is described in terms of the Left (L) and Right (R) channel. From these we can get the Mid and Side channels with the following calculation:
Mid = (L+R)/2
Side = (L-R)/2
The Mid channel is also often called "Mono" and Side "Stereo" (that's nice, the first letters are the same!). The Mid channel contains the signal that is in the center of the stereo mix, and the Side channel contains the rest (everything that is on the sides of the mix). By seperating them, we have the opportunity to process those signals independently.
Should we wish to return from Mid/Side format back to Left/Right, then we can recreate the Left channel by summing the Mid plus the Side, and the Right channel by taking the Mid minus the Side, as follows:
Left = Mid + Side
Right = Mid - Side
Any conventional stereo signal can be converted to Mid/Side stereo, and back again, with no loss of information! Using the Mid and Side channels to treat them differently gives us many creative opportunities and gives a tremendous amount of control over the stereo spread.
So why we want to use that in a compressor? Well, there are a few basic possibilities that mastering engineers use to control the amount of stereo spread in a track. By compressing only the Side and leave the Mid unaltered, it will sound more 'mono' without introducing phase problems.
Alternately, if you would only compress the Mid and leave the Side unaltered, you will get a more compressed sound without touching the stereo spread.
FabFilter Pro-C gives you both options and anything in between.