The term "rain check" refers to a situation where someone postpones or defers an invitation, offer, or event to a later time. It originally comes from the practice in sports, particularly baseball, where a ticket holder for a game that is rained out receives a voucher (or "rain check") allowing them to attend a future game instead. In everyday conversation, it signifies that although someone cannot accept an invitation or offer at the moment, they would like the opportunity to do so later.
The term "rain check" originated in the United States in the late 19th century. It was used in the context of baseball games where unfavorable weather conditions caused a match to be canceled. Ticket holders were given a "rain check" as a promise that they could attend a future game.