A multi band compressor is actually 4 individual compressors each tuned (using electronic crossovers) to operate on  a limited portion of the spectrum ... kinda like the way a 3-way (or in this case a 4-way) speaker does.

What this does is to actually control dynamic range without adding much coloration.  Normally if you used a sinlge full range compressor and you hit it with a strong bass note or kick drum smash, it will clamp down on all frequencies.  So every time you kick that compressor will put it down like you do want but it also will pull down the highs (think cymbals) which you would really rather leave alone.

By splitting the compression into 4 bands the lows, low mids, mids and highs are all seperate so now that kick wont cause your cymbals or the sparkle in your voice to be sucked out.  So to simplify, this means that you can use much more compression without compromising the sound.  And in a PA system that can mean that you can actually play it louder than you would normally expect for a given sized speaker system

Of course you can trick it up and customize it to purposly color your tone if you like.  But just using it straight off the patch list is easy and can really make things louder when you need to do that.