This is the promise to complete an unfulfilled order or task at a later or more convenient date.
People don’t like to do anything in the rain. Therefore they pass along a metaphorical voucher—a rain check—to affirm their intent to complete the task. Of course, tangible ‘rain checks’ are also often handed out, say, at an outdoor event postponed by bad weather, or at a store when an item has sold out.
A promise that an unaccepted offer will be renewed in the future, as in ‘I can't come to dinner Tuesday but hope you'll give me a rain check.’ This term comes from baseball, where in the 1880s it became the practice to offer paying spectators a rain check entitling them to future admission for a game that was postponed or ended early owing to bad weather. By the early 1900s the term was transferred to tickets for other kinds of entertainment, and later to a coupon entitling a customer to buy, at a later date and at the same price, a sale item temporarily out of stock.