If they all make the same decision, they're successful. But, if there's a miscommunication or treachery causing some generals to attack while the others retreat, then the battle is lost. These types of problems are known as Byzantine faults.
With any computer system that has multiple nodes, each node could be considered a general. The system's Byzantine Fault Tolerance refers to whether it can keep working even when some nodes go down or intentionally try to deceive it.
Importance of Byzantine Fault Tolerance
From a computing perspective, Byzantine Fault Tolerance is important because it means a system can keep functioning even if certain components stop working. Anything that uses a computing system, such as an airplane or a space probe, needs to be able to work when not all of its nodes are at 100%.
If you invest in cryptocurrency stocks or individual coins, there's another reason it's worth learning about this subject. Byzantine Fault Tolerance is a crucial element of the blockchains that handle cryptocurrency transactions.