Consensus protocols are a solution to the double-spend problem: the challenge of preventing someone from successfully spending the same digital money twice. The hardest part about this problem is putting transactions in order: without a central authority, it can be difficult to resolve disputes about which transaction comes first when you have two or more mutually-exclusive transactions sent around the same time. For a detailed analysis of the double-spend problem, how the XRP Ledger Consensus Protocol solves this problem, and the tradeoffs and limitations involved, see Consensus Principles and Rules.
Consensus Protocol
An explanation of how the double spend problem is solved.