A marker is an IOU that the player signs over to the casino in exchange for gambling chips. It's a negotiable monetary instrument that looks similar to a bank check; in fact, it can be used as an actual check, since the casino can run it through the player's bank account if necessary, the same as a personal check. This happens on occasion when a player fails to redeem a marker in the time allotted.*
Cash or chips are drawn at the tables or from the cashier cage based on either a player's front money (cash or a check that a gambler deposits with the casino) or a player's line of casino credit (a short-term loan based on how much money the player has in his bank accounts). When the player draws the chips, he signs the marker as a receipt. If the marker is drawn on front money, the player doesn't have to buy it back; it's the player's own money on deposit in the cage, which the casino takes if the player loses. However, if the marker is drawn on his credit line, he has to pay up, either at the end of his trip or within a specified amount of time.
If he doesn't pay up, the casino deposits the marker in his bank account, whereby it's treated like any other personal check. If the marker bounces, then the casino can press charges to recover the money.
The sky's the limit with markers, all depending on how much front money or casino credit a player has. Markers for $1 million are not uncommon. The lower limit is usually $500 or so.