To "take a rain check" means to postpone something until a later time. Here's an example:
- "Would like to go for lunch with me today?"
- "I'm afraid I can't. I have a meeting. I'll take a rain check, though."
Here, "I'll take a rain check" means: I'll definitely go for lunch with you at a later date.
To be "given a rain check" is to be told by someone else that something is postponed.
I believe that the phrase "rain check" originated in the US sport of baseball. When it was raining, games were sometimes postponed. Fans who'd come to see the game were given "rain checks", which were tickets allowing them to come back and see the game whenever it was rescheduled.