I had never heard this term until today and found it interesting. What? It's Monday. Get to work.
Mean time between failures (MTBF) is the predicted elapsed time between inherent failures of a system during operation.  MTBF can be calculated as the arithmetic mean (average) time between failures of a system. The MTBF is typically part of a model that assumes the failed system is immediately repaired (zero elapsed time), as a part of a renewal process. This is in contrast to the mean time to failure (MTTF), which measures average time between failure with the modeling assumption that the failed system is not repaired.
The definition of MTBF depends on the definition of what is considered a system failure. For complex, repairable systems, failures are considered to be those out of design conditions which place the system out of service and into a state for repair. Failures which occur, can be left or maintained in an unrepaired condition, and do not place the system out of service, are not considered failures under this definition