The definition of take a rain check is:
(verb) to politely refuse an offer, with the possibility that you may accept in the future
A: I’m having a dinner party tomorrow. Can you come?
B: Sorry, I’ll have to take a rain check, I already have plans.
A: Okay, no problem!
Son: Dad, you promised to take me fishing!
Dad: Sorry son, I’m very busy with work. Would you take a rain check?
Son: I guess so. Can we go next week?
When I couldn’t go to my friend’s birthday party, I took a rain check instead.