In Poker, a drawing hand is a hand that is not yet “complete”; that is, one which does not yet rank highly, but which may later, depending on what cards a player receives. This contrasts with a made hand – a hand which is already somewhat strong.
An illustrative example from Texas Hold ’em: if Alice holds A♣ K♣, Bob holds 6♦ 7♦, and the flop comes 5♠ 8♠ K♥, then Alice has a fairly strong “made hand” (a pair of Kings, with an Ace kicker), while Bob has a drawing hand: an open-ended straight draw. If allowed to see the final two community cards, Bob can expect to catch a 4 or a 9 (thus completing his straight and winning) about a third of the time.
Whether to continue with a drawing hand is usually a function of pot odds. Typically, if a player with a strong “made hand” suspects another player of being “on a draw”, the player with the made hand will make a strong bet, so that it is mathematically incorrect for the other player to “chase”.