A Mid-Side Effects Processor lets you target two different parts of the stereo field. The outside and inside (center) of the stereo field.  These two ranges are preset and you don't have the option to change them, nor do you know specifically what the ranges are.  From my experience, I would say CENTER usually covers roughly the range of L70 to R70.  The SIDES are L to L71 and R71 to R.

WHY WOULD YOU NEED THIS? WHEN WOULD YOU USE THIS?
1. I use a Mid-Side Processor mostly to check the stereo field of a mix.  I use the Mid-Side 5-Band EQ and solo the SIDES.  If I don't hear much musical content on the sides (or only light reverb), the mix has a weak stereo spread and is basically a mono mix.  I then either ask for a remix or boost whatever is on the SIDES (which usually doesn't achieve much).

2. Sometimes a client mixes their stereo guitars (or background vocals) very loud and they overtake the entire song.  A Mid-Side 5-Band EQ can easily fix this problem by cutting only the SIDES down a few dbs.  Or by boosting the CENTER.

3. If the lead vocal is buried by guitars and the guitars are stereo panned well, sometime a Mid-Side 5-Band EQ boost around 2-3k in the CENTER will bring the vocal out.  You could also combine this with a SIDE cut.

Note - For mastering, I only use a Mid-Side 5-Band EQ, NOT any other Mid-Side Processors.  And when I do use it, it's only for the few instances I mentioned above.