To take a rain check is to politely decline an invitation or offer in the moment while expressing a genuine intention to accept it at a later date. 'Can you come for dinner on Saturday?' 'I can't make it, but can I take a rain check?' implies: I want to come, I can't right now, let's do it another time. It is an important social phrase because it distinguishes a postponement from a refusal.
The origin is entirely American and entirely literal. In the 1880s, Major League Baseball games were called off when it rained. Spectators who had paid for tickets but had their game rained out were issued a voucher — a 'rain check' — that allowed them to attend a rescheduled game or another game of the season at no additional cost. The voucher guaranteed their admission was not wasted.
The retail industry adopted the term in the early 20th century. When a sale item sold out, shops would issue customers a 'rain check' guaranteeing them the sale price when the item was restocked. From there, the phrase moved into everyday social use, where the 'voucher' became metaphorical — a social understanding that an invitation remained open.
In origin, yes. The phrase is American and is most commonly used in American and Canadian English. In British English, you might more typically say 'can we arrange another time?' or simply 'I'll take you up on that another time.' The rain check phrase is understood in Britain but sounds distinctly American.
Socially, yes — a light one. Taking a rain check implies genuine intent to follow through. Using it repeatedly without following up moves from polite deferral to avoidance. The social currency of the phrase depends on occasional redemption.