Table stakes is the standard method of playing poker for money. The phrase means that your stakes (the amount of money you are wagering) is the amount of money which is on the table in front of you. You are not wagering any more, so you cannot be required to pay any additional money; and you are not wagering any less, so you cannot "protect" part of your chipstack by claiming you are all in when you really aren't.
This method evolved to battle the concept of players being forced to reach into their pocket for additional money in order to call a bet, or even worse, being unable to call a bet due to lack of funds, and being therefore forced to fold, which is patently unfair. If a player had to fold if they were short of funds, a rich player could simply sit down at a table with, say, a million dollars in chips in front of them and then push all in on every hand. With no player able to call that bet, the rich player would simply win every hand, since the poor players would be forced to fold.
This "forced to fold" concept is often seen in movies about poker in the "Old West", where the banker says "I bet $1000", and the rancher says "I don't have that kind of money - but I can put up my farm!". When the banker refuses, the rancher folds and the banker laughs all the way back to his bank. Or, more likely in the movies, the banker accepts the farm as collateral and then wins the hand -- and the farm.
The concept of table stakes affects poker betting in two ways:
All in[]
Because table stakes says the amount you are wagering is not any more than the chips you have on the table in front of you, you cannot be forced to reach into your pocket to bring out cash in order to call a bet, nor can you do so on your own volition. If another player bets more than you have, you may call the bet by pushing the remaining chips you do have into the pot, calling their bet by going all in.
In order to be fair to other players, however, when you go all in for your remaining chips, the pot for which you are contesting is reduced in size until it is the same size it would be if all the other players remaining in the hand had the same amount of chips left that you had, as if they had all gone all in with you at the same time for the same amount. Effectively, this means that you cannot win from another player more chips that you have in front of you to start a hand.
Remaining betting, or the remainder of the chips bet by other players, is now placed in a side pot, for which only the other players are contesting. Being all in, you have no claim to the side pot, and it goes to the player who is still involved in that side pot who has the best hand. Essentially, once you go all in, you are sitting out of the rest of the hand as the other players continue playing for the side pot. Only once the hand is over and the side pot has been awarded do you re-enter the game and turn over your hand to determine if you have the best hand for the main pot.
On a practical matter, this rule is the reason why you cannot buy additional chips during the play of a hand. If you wish to purchase additional chips and grow your stack, you must do so prior to your initial hand being dealt to you. Otherwise, players could sit down with $10 at a no-limit hold 'em table, play normally and lose a buck or two, wait for pocket aces, then buy $500 and push it all in and win a lot of money. You must decide how much money you are willing to risk on the poker sesstion, at this poker table, prior to having any cards to look at. Then, you decide how much of your current chip stack you want to risk on any given hand or betting round.
Chips Remain On The Table[]
Because table stakes says you are not wagering less than the amount of chips in front of you on the table, you are unable to "protect" the chips you do have by simply refusing to call a bet by putting any more chips in the pot. If you refuse to call but you have chips in front of you, you must fold your hand. If you wish to continue in the hand, and a bet has been made to you, you must either call the bet, raise it, go all in for your remaining chips, or fold.
By extension, you are not allowed to remove chips from the table during a session of poker. In a way, this is simply you "Refusing to use your chips to call a bet" in the future. You cannot win a few big pots, then slide that extra $100 chip you just won into your pocket. While you are playing, your winnings are part of your table stakes, and you cannot change that. You are entitled to leave the table at any time and cash out, thus putting your chips in your pocket, but when you leave the table, you are generally not allowed to rejoin it until some specified amount of time has passed, or unless you are willing to rebuy in for the amount you took when you left. House rules differ from casino to casino about when you would be allowed to re-enter the game, but the general principle remains the same.
Removing chips from the table during play is called ratholing, and it is not only against etiquette, it is against the rules in nearly all casinos, and may be cause for expulsion from the table or the casino. Casinos, of course, recognize that beginning players do not realize this, so they will allow you to stay if you simply agree to put the chips back on the table that you took off.
The basic premise behind this rule is to be fair to the other players. If you hit a lucky hand and win $100 from each of five other players, then if you want to continue to play, you must continue to put this newly-won money at risk and give them an opportunity to win it back. You cannot pocket it, then continue playing with only $5 in chips left, and go all in, which would only give them an opportunity to win back $5 of that money.
An exception to the "chips remain on the table" rule is for "incidental expenses". In nearly all casinos, you are allowed to pay for drinks or meals, or to tip waitresses and other casino employees, using chips from your stack. These amounts are generally so minimal that they do not materially affect your chip stack.
Chip Transfers[]
Table stakes as a concept is also the reason most casinos do not allow you to give chips to another player at the table (this practice is called chipping). The amount of money you are wagering cannot be reduced by arbitrary amounts simply because you want to stake another player. You must continue to wager your at-risk money until you decide to leave the table entirely.
When you leave the table, you are usually allowed to give your chips to anyone, at the table or not (if there is a buy-in limit and the transfer would put the receiving player over the limit then it will not be allowed). You are also allowed, during play, to stake another player with money taken from your pocket. But you cannot remove chips from your stack during play, so you cannot simply move some of your chips to another player.