A floating rotor is an assembly consisting of a hub and a rotor that are attached by a "loosely" fitted attachment that allows the rotor to move side to side and a bit forward and backward. Here's a close up of a randomly selected example. The rotor is in the lower portion of the picture and the hub is in the upper portion. The blue part is the attachment that I'm talking about.

Very nice explanation and the picture is worth 1,000 words. Thank you!

I always wondered what those silver "disks" were on my hub/rotor. Now I know, though I have to wonder, why? If the calipers can float, what is the advantage of the rotor floating, too?