I can't really give the best definition, but I know the floating deck is definetly easier to adjust and usually doesnt scalp as back since it has play to move up and down without moving the whole mower. It usually comes with more scalp wheels as well so it's almost impossible to scalp with it althought I've never used one.
A fixed deck is attached to the tractor part of the mower by bolts. The height can be adjusted either from the bolts on the back or from the casters on the front of the deck. A floating deck is not fixed to the tractor part of the mower. The height is adjusted by mowing 4 pins on top of the deck. In my opinion, unless you're cutting extremely rough lawns, a floating deck is too complicated, and there are a lot more parts to break on a floating deck than on a fixed deck. I feel that unless you have a 61"+ deck, a fixed deck is the best option.