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; it can actually be run through the player's bank account if necessary (for example, if the player fails to pay it off in the time allotted).
Cash or chips are drawn at the tables or the cage based on either a player's front money (cash or check deposited with the casino) or a player's line of casino credit. The player draws gambling money, then signs a marker as a receipt. If the marker is drawn on front money, the player doesn't have to buy it back; if it's 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 its bank account, whereby it is 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.