Have you read this? https://bitcointalk.org/oldSiteFiles/byzantine.html

tl;dr The Byzantine Generals' problem is a problem of agreement, where no one party can come to agreement with another without fear of misinformation. The longest blockchain (in terms of hashes to produce) requires at least 51% of the network. Therefore the majority of the network agrees on the content of that blockchain. In Bitcoin's case the blockchain contains transactions, which are Bitcoin. Anyone can easily verify the blockchain's parts, nobody can practically alter part of an existing blockchain without invalidating it, and nobody can practically create a substitute.

The blockchain is an example of proof-of-work. It is a practical solution to the Byzantine Generals' problem because although it is possible to deceive network participants or cripple the network, it is prohibitively difficult.