Meaning 1 ►▼
The game was postponed because of rain. (The game could be postponed for any reason, but the term is "rain check".) The rain check itself is the ticket that can be exchanged for a ticket at a later date.
The Phillies' game was postponed because of rain, and the spectators were given another ticket for a future game.
Meaning 2 ►▼
a postponement with a promise of a future meeting
"Something has come up, and I can't make our luncheon meeting. How about a raincheck? "