A rain check was first a ticket. If a baseball game was rained out, it was good for a later game. Around 1889 teams began to use a stub on the original ticket instead. The term was in use by 1877. Today it means a promise to accept an offer at a later time: “Can I take a rain check?”
Baseball still works this way. A rained-out game is played on another date, sometimes as one game of a doubleheader. The Detroit Tigers tell their fans: “If a game is postponed due to a rainout, PLEASE HOLD ON TO YOUR TICKET!”