Casino credit is an interest-free line of credit offered to gamblers for use in the casino. After a line is approved, markers can be taken out against it, either at the tables or the cage.
Casino credit is essentially a ceiling based on what your bank account can cover and what you've requested from the casino. This varies from other consumer credit, like credit cards, which have limits based on what you can conceivably pay back over a period of years. This is because your markers are essentially counter checks against said bank account.
If you win, you should pay off your markers before you leave. Failure to do so is called "walking with the chips", and is is frowned on by the casino. If you lose, you can either pay the marker off with a check or cash at the casino, or allow the casino to deposit your marker. This deposit will happen after 7 days for amounts < $1,000, and 14 days for amounts > $1,000 (varies by casino).
At the Rio, the casino I play at most often, the minimum line they will extend is $2,500. Your hotel may be similar, or vary.
When you use credit instead of cash, they know what you play, and they know how much you can play. This is supposed to get you more comps. Note: I have not verified this firsthand, yet.
One might ask, "Why would a casino offer people an interest-free loan?" The answer is that credit doesn't seem as tangible as cash, so people usually gamble more, and more often, when using credit. Also, it's not exactly a loan, per se. It's more like them agreeing to take a post-dated check.
Used wisely, credit is a powerful tool that will increase your visibility to the casino, and allow you to avoid having to carry large amounts of cash or bring a cashier's check as "front money". Abused, it can drain your bank account very quickly.