To refuse an offer or invitation but say that you might accept it later (said to someone who has invited you to something that you cannot attend now, but would like to attend at a later time.) ‘Are you coming for a drink?’ ‘Can I take a rain check?—I must get this finished tonight.’

Thanks for all answers, they are very clear. :)

It can mean different things. As Chelsea said, it means to reschedule. "Let's go to lunch. I'll pay." "Sorry, I'll have to take a rain check." It is also a piece of paper that guarantees you can have the sale price on an item in a store if it sold out before you got to the store. So if you go to buy the 1/2 price hair dryer but there are none left, the store can offer a rain check, a piece of paper that gives the name of the product and the price you will pay when it comes back in stock even if the sale is officially over. It is also the replacement of tickets for an event (concert, sporting event) that gets canceled.

i think it's more like "reschedule" if you are going to go on a date with someone, but then you have to go to work, you can ask for a rain check for another day