The huge size is not limited to carbon ceramic, that's just an attribute of most high performance cars' rotors.
Carbon ceramic brakes are more expensive because the exotic compound does a much better job of dissipating heat than traditional steel rotors. Because they are able to dissipate heat faster, they do not get "soft" as quickly as other brakes. Soft meaning that they do not brake as hard and stop the car as quickly.
When brakes get "soft" they are typically too hot to operate. Brakes work by converting physical energy into heat. In some cases, they can also convert this into light energy, as is often the case with carbon ceramic brakes when they glow red.
Although brakes can also get "soft" by boiling your brake fluid or getting air in the lines, you will typically see this due to overheated rotors as opposed to brake fluid issues.