1. [techspeak] A flag on some processors indicating an attempt to calculate a result too large for a register to hold.
2. More generally, an indication of any kind of capacity overload condition. “Well, the Ada description was baroque all right, but I could hack it OK until they got to the exception handling ... that set my overflow bit.”
3. The hypothetical bit that will be set if a hacker doesn't get to make a trip to the Room of Porcelain Fixtures: “I'd better process an internal interrupt before the overflow bit gets set.”