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Describes a system where there are no centralized points of failure (eg. a pillar that holds an entire structure up), or an organization that has no central authority figure. Bitcoin is an example of a decentralized system.
A byzantine fault is where an error has occured, yet a computer system does not know due which component/what failed to the lack of information and continues to iterate on a given instruction.
It is the "second layer" or an off-chain of payment protocol that operates on top of a blockchain. Payments on this network do not need block confirmation and it will be instant.