Floating rotors are identified by the 2 piece design of the center hub and outer disc friction surface attached by symetrical number of fasteners that allow the disc to "float a bit" from the center hub. This is in sharp contrast to the single piece rotor stamped and machine and somewhat unforgiving if caliper pistons or pads get contaminated or start wearing unevenly. Personally I like the whirring sound of floating rotors as well, they are a very basic sound that many metric sportriders have enjoyed for many years.
There are several advantages one being the additional movement allows more even contact with the pad surfaces when caliper is activated which makes for better braking and even pad wear. Another is less "pulsing" feel at the brake levers, as full floating rotors allow the caliper to even out the contact surface and ultimately adds a bit better stopping power. The second advantage is cosmetic, in that the hub can be finished differently, and ideal friction disc materials may be selected, while the hub can be made more "trick" if not tied directly to the friction disc. Black, Alloy/Billet look or shiny chrome hubs can all be had with floating rotors. The fasteners can be chrome, stainless, black to further the look angle.