Comp is short for complimentary. Casinos give services, rooms (huge suite with a butler), food (choice seats at a gourmet restaurant), show tickets, and reimbursement for airline tickets for free or for good discount price to entice them to come to their casino and gamble.

Comps can be obtained by all players, high roller or otherwise. Best thing to do is simply to ask for it after you have played a while.

Casinos determine your comp eligibility like this: average bet x decisions per hour x hours played x house advantage. Example: Blackjack - $20 per hand - 4 hours played - 70 hands per hour - house edge is 2%: 20 x 4 x 70 x 2 / 100 = $112. A casino usually returns 40 % in comps. In this example they will give you a comp for $45 or a dinner for two.

Go to the guest service desk or cashier and ask for a VIP, slot club or player's club card. Use this card every time you play and get a card from every casino you visit. While using it you are being rated. The casino staff will evaluate you based on the amount you bet, which games you play, and the amount of time you spend on each game.
Online casinos offer comps as well. The most famous online casino to offer comps is the Sands of the Caribbean Casino.