From another forum:
"Not sure if you're looking for an origin of the word, or what it implies.
I don't really know why the word BINGO is used, but it holds a very important meaning in military aviation. In general, its a pre-briefed amount of fuel that, when reached, you need to go home.
For example, in the hornet world, we typically will brief a 3500lb bingo (VFR), giving us 1500 lbs to get home, and 2000 lbs of slush - pattern work, potential delays due to other traffic, etc..."
http://www.avcanada.ca/forums2/viewtopic.php?t=26117