A hard fork in the context of Bitcoin occurs when a change is made to the protocol that is not backward compatible. This means that the new version of the software is not compatible with the old version, resulting in a permanent split in the blockchain. This leads to the creation of a new cryptocurrency with a new set of rules, while the original cryptocurrency continues to exist with its original set of rules. Hard forks can be contentious and can lead to disagreements within the community about the direction of the cryptocurrency.