A casino makes profits the same way any other business makes profits -- by taking in more money than it expends in fixed and variable costs.
Casinos make their profits mainly by the fact that their gambling games are rigged against the player. This is not to say that they cheat, it is just to say that this is how the games are set up. Each game is set up in such a way that "the house" is guaranteed to win over the long term.
So the casinos have this guaranteed stream of income. In order to make profit, all they have to do is ensure that they spend less than they take in. This means that they have to avoid paying their employees too much, etc, just as any other business would have to do.
A casino makes profit by ensuring that cash inflows are always more than the cash outflows. Though the amounts that people sometimes win at casinos may seem large and give an illusion that a casino gives away all that it collects and hence makes no profits, casinos are very profitable. Gambling is a play of probabilities and casinos do extensive research to calculate the probabilities that a person may win and ensure that how much they charge as a fee to play any game is many times what may have to be given to a lucky winner.
In addition, the hotels and the hospitality industry that is run in the casino to keep clients comfortable provide a large portion of the profits that they make.
Casinos make profit in three ways. First is through the main activity of the casino which is gambling. The various escarpments installed in the casino and odds of winning on these installments are designed to ensure that on average the total average payout of winnings to the people betting in the casino is less than the total amount of money put on bets. In this way some people may win substantial amounts on a particular day but loss to the casino due to their winnings is less than amounts received from a much larger number of people who loose.
Second, casinos may charge an entry fees. Finally casinos may also make some profit on sales of food and beverages they provide in the casino.