Table stakes is simply the (nearly universal) rule that a player may only wager money they have on the table at the beginning of a hand. Usually it also implies that money may not be removed from the table at any time (exceptions are made for tipping), although money may be added to one's stacks between hands. A player who goes all-in at a table stakes game may not continue to bet, and is eligible only for the main pot. Sometimes "table stakes" also implies no-limit play.
A game that allows you to play with only the money you have on the table. In live game, both checks and cash count as playable. Basically, table stakes doesn't allow you to pull out your wallet and put more money into a live pot and also doesn't allow you to "bet the farm," since you'd have to go get the deed and bring it to the table before you got involved in a hand.
A popular rule that states you canâ€™t add money to the bankroll you have on the table during a hand. As a corollary, you canâ€™t be forced to fold by someone with a larger bankroll than you, and instead a side pot is created for bets exceeding your contribution. This is a universal rule in casino poker.