The kettlebell clean begins as a kettlebell swing that you bring into the rack position. A single kettlebell clean's main use is as preparation for a single kettlebell press or other overhead move that begins from the rack. If you're looking at what's getting worked, think about the swing.
The skill of racking a kettlebell clean is an exercise in coordination (timing, finesse, quick turning on and off of muscle tension) more than for any particular muscle.
Those who choose the clean by itself as a power or conditioning tool generally perform it with two kettlebells.
The brachioradialis seems to get worked pretty intensely. I find that in my 5x5 cleans, it's the arm fatigue that occurs first, not that I yank very much on the bell as far as I can tell. Was wondering if heavier cleans could significantly help improve pullups.