A single piece rotor is machined from a single piece of metal.
Pros - least expensive method of manufacturing
Cons - If the machining isn't accurate, you can have disk surface run-out relative to the brake hat or the hub mounting surface
Cons - heavier than a two piece
A two piece rotor has a brake hat that is machined from a seperate piece of material from the rotor. The rotor remains cast, but the hat is usually machined from billet aluminum. The hat is then mounted to the rotor one of two ways, either solid or 'floating'. When solid mounted, the hat is bolted firmly to the rotor at multiple tabs machined in the rotor. When 'floating', rather than bolting the hat firmnly to the rotor, there are pins than locate the rotor radially, but allow for some misalignment axially. Under severe braking, the rotor can distort. By allowing the rotor to float, pad to rotor contact is optimized.
Pros - improved braking under severe conditions
Pros - the pins act as insulators - heat remains in the rotors and does not transfer to the hat
Cons - more expensive to produce
Two piece rotors are overkill for the street, but common in racing. They do look awesome however.
One piece - both rotors on the left:
Two Piece - rotor on the far right: Notice that the hat is gold and the many small silver mounting bolts that hold the hat to the cast rotor.