A rain check usually has nothing to do with rain: it's a promise to do a canceled activity in the future.
Originally, a rain check was a ticket given to people who went to an event that was canceled because of rain. The rain check would get you in to another game in the future. These days, a rain check usually has to do with rescheduling. If you’re sick but have plans to hang out with a friend, you could ask for a rain check. This is a nice way of saying, "I can't do this now, but I will later."