A floating rotor from what I've put together looking at mine is a two piece rotor held together by (for lack of a better word) rivets. It allows a bit of movement but I'm not 100% sure why.
Floating rotors allow for the thermal expansion of the rotor without binding it to any other non heat-affected part. That reduces the tendency to distort laterally ("potato chip") when hot. It also allows the contact surface of a bent or heat distorted rotor to run straight through the pads while the "wiggle" is put at the rivets where it does no harm.