The FLP impossibility result, named for Michael Fischer, Nancy Lynch, and Michael Paterson, is one of the most important negative results in distributed computing. In their 1985 paper “Impossibility of Distributed Consensus with One Faulty Process,” published in the Journal of the ACM, they proved that in a purely asynchronous system, no deterministic consensus protocol can guarantee agreement if even a single process is allowed to fail by crashing.
The key word is asynchronous. In their model, messages are eventually delivered but there is no bound on how long they take, and processes have no synchronized clocks. Under these conditions there is no way for a correct process to tell a crashed process apart from one that is merely slow. The paper shows that an adversary can always keep the system in a state where a decision has not yet been forced, delaying agreement forever.
The result does not say consensus is impossible in practice. It says no algorithm can be both always correct and always terminating in this model. Real systems escape the trap by adding assumptions the model forbids: timeouts and partial synchrony (as in Paxos and Raft), or randomization, both of which trade the absolute guarantee for one that holds with overwhelming probability or under realistic timing.
FLP defines the boundary that every practical consensus and replication system is built against, which is why it remains a standard reference for understanding why fault-tolerant coordination is fundamentally hard.