In card games, your hand is the set of cards dealt to you: the two hole cards in Texas Hold’em, the first two cards in blackjack, the five cards in draw poker. The same word also names a single round of play, so “twenty hands of blackjack” means twenty deals from start to finish.
Context tells you which sense is meant. “Show me your hand” is about the cards; “one more hand” is about time at the table. For operators, the hand is the basic unit of table-game data. Hands per hour, average bet per hand and hand-history logs feed game analytics, help settle disputes and set the pace of live dealer tables.