To tap out is to lose your whole bankroll and be unable to keep playing. Before a session, players either decide how much money they are prepared to spend or simply play with everything they have on them. Either way, that sum is the bankroll. Tapping out means it is gone, and the session ends there, at least for that night.
Nobody likes hearing the phrase, which is why bet sizes that match the bankroll matter so much. Small stakes relative to the total make a session last longer and make tapping out less likely. Players at a table may describe the same situation as being down to the felt.
Tapping out and player protection
Online, a player who taps out can be tempted to redeposit immediately. Deposit limits, reality checks and clear session summaries help players stick to the budget they set, and repeated tap-out-and-redeposit cycles are a recognised risk signal for responsible gambling teams.