Table stakes is the rule that a player may not add chips to, or take chips out of, play while a hand is in progress. Nobody can reach into a pocket mid-hand and put extra cash on the table, and nobody can set part of their chips aside for safekeeping unless they leave the game and take all of their chips with them.
The rule limits how much a player can lose in a single hand, and how much other players can be pushed to bet. It also levels the field: a player with a far bigger bankroll cannot bully opponents into stakes they are uncomfortable with. A player who runs short can still go all-in with what is in front of them. Between hands, topping up or re-buying is fine, provided the game’s rules allow it and the total stays within the maximum buy-in.
Table stakes in online poker
Poker software enforces the rule automatically: only the balance a player brings to the table can be used in a hand, and top-ups apply between hands within the table’s buy-in range.