In fault-tolerant computer systems, and in particular distributed computing systems, Byzantine fault tolerance is the characteristic of a system that tolerates the class of failures known as the Byzantine Generals' Problem, which is a generalized version of the Two Generals' Problem - for which there is an unsolvability proof - wikipedia 
Byzantine failures are considered the most general and most difficult class of failures among the failure modes. So called fail-stop failure mode occupies the simplest end of the spectrum. Whereas fail-stop failure model simply means that the only way to fail is a node crash, detected by other nodes, Byzantine failures imply no restrictions, which means that failed node can generate arbitrary data, pretending a correct one, which makes fault tolerance utterly difficult.
The phrases interactive consistency or source congruency have been used to refer to Byzantine fault tolerance, particularly among the members of some early implementation teams.
The objective of Byzantine fault tolerance is to be able to defend against Byzantine failures, in which components of a system fail with symptoms that prevent some components of the system from reaching agreement among themselves, where such agreement is needed for the correct operation of the system. Correctly functioning components of a Byzantine fault tolerant system will be able to provide the system's service, assuming there are not too many faulty components.
The following practical, concise definitions are helpful in understanding Byzantine fault tolerance:
# Byzantine fault
Any fault presenting different symptoms to different observers
# Byzantine failure
The loss of a system service due to a Byzantine fault in systems that require consensus
The terms fault and failure are used here according to the standard definitions originally created by a joint committee on "Fundamental Concepts and Terminology" formed by the IEEE Computer Society's Technical Committee on Dependable Computing and Fault-Tolerance and IFIP Working Group 10.4 on Dependable Computing and Fault Tolerance. A version of these definitions is also described in the Dependability Wikipedia page. The type of system services which Byzantine faults affect are agreement (a.k.a consensus) services.