If you run espionage games, these are well-nigh essential bits of tradecraft... and if you run any kind of game in which radio has been invented, a numbers station message or two can add an air of mystery or intrigue to whatever might be going on. It might even have something to do with your plot - or it may be a complete red herring.
So, if you didn't crouch over your shortwave radio during the 1970s (which is when I found them on the airwaves) what is a numbers station anyway?
The short answer (at least officially) is that nobody knows. Or at least, not that they'll own up to. The most common interpretation is that they carry coded messages which could only be interpreted by the intended recipient, hunched over his radio with a one-time pad at the time he expected his controllers back home (wherever that was) would be transmitting his instructions.
So, how to use them? It could be something that your characters intercept. Or they find that an otherwise innocent-looking fellow has a shortwave radio and a one-time pad hidden away, so perhaps they'll be able to find out what he is being told to do. Or maybe they are the ones awaiting orders... you'll have to work out a way for them to decode whichever message is for them in that case.
Have fun. Meanwhile I shall have to explain to my family why I'm listening to a numbers station!