The problem is how to achieve agreement (“consensus”) on the truth when at least one person is actively lying and trying to disrupt the truth. In the context of digital money, it’s how you prevent the same coin being spent twice when manipulating digital information is easy.

A related problem is a Sybil attack, where a decentralized peer-to-peer system that is truly open makes it easy to generate new identities and overwhelm the system, so simply relying on the majority of accounts to agree on truth can still be subverted by a motivated attacker.

Bitcoin was a novel solution to this problem by using “mining”, or raw computation power, as a mechanism for enforcing consensus. This made Sybil attacks worthless as the only thing that truly matters in Bitcoin is computation power, which is expensive, and an attacker would need 51% of the power to attack the network.