Byzantine Fault Tolerance (BFT) is the property of a system that allows it to reach consensus despite failures or errors.
Byzantine Fault Tolerance is a property of a distributed computer system, where components of the system may fail and there is imperfect information on whether a component has failed. In terms of cryptocurrencies and blockchain, BFT is a characteristic of a system that assures consensus will be reached even when some nodes disseminate false information or don't perform their duties.
The term comes from a problem in distributed computing known as the Byzantine Generals Problem, where different generals (nodes) must agree on a common battle plan (consensus), even though some generals may be traitors (faulty nodes). In the context of blockchain technology, BFT is a vital property as it assures the integrity and reliability of the blockchain, even in the face of faulty nodes.
Practical Byzantine Fault Tolerance (PBFT) is used in some blockchains to prevent double spends and achieve consensus. For example, the consensus algorithm used by Bitcoin, called Proof of Work (PoW), is Byzantine Fault Tolerant. It allows the Bitcoin network to function and reach consensus despite the possibility of nodes failing or acting maliciously.