Computers set limits internally on how big numbers can be when they're keeping track of stuff.
Your developers had given each game a number to identify it. So your first game was #1, the 40th game was #40, and so on.
The limit for how big the number could be was a bit over 2 billion, and your players have just now played a bit over 2 billion games, and so that id number suddenly exceeded the computer's internal limit. Specifically, the limit was 2147483648, so basically it crashed on game #2147483649, which is the next id after the last acceptable one (notice the last digit is 1 higher.)
I'm simplifying slightly but that's the idea. It'll be fixable by essentially using a different format for the id number so that the limit is higher, much like telling the computer "use a higher limit for this particular number, it's special."