The reference is to the game Bingo, where you have a card with random numbers on it and a caller calls out a series of numbers that you can check off if you have them. As soon as someone has five in a row they shout Bingo,  which means in effect: I have it. I've won. The game is over. 

Randomly chosen numbers, usually up to 75 or 90, are called out by a banker.  The first player to achieve a card (or a line) in which all of the numbers have been called shouts bingo  or house  and collects the entire stake money, usually less a specified percentage, if that is permitted by local law.