When used in Las Vegas, it is short for compensation. Gamblers earn a certain number of comps depending on the amount of money they wager per hour of gambling (whether they win or lose).

High rollers might receive a free suite at the hotel, while low rollers may earn something like a free breakfast buffet.

(verb) A musical figure of speech used especially in jazz performance which refers to the act of playing chords, usually in parallel with a solo melody. Thus comping is done with harmonic instruments like a piano or guitar. Good jazz comping is rhythmically interesting, harmonically varied and provides appropriate background to the melody and foreground to the bass line and percussion. Origin unknown; perhaps an abbreviation of compose.