Hard Fork is a method of changing the specifications of a blockchain, an update that is not backward compatible.
The blockchain diverges, and then without the divergence converging, a different cryptocurrency is created from the original one.
Unlike a soft fork, a new blockchain may be created that is not compatible with the previous version.
Hard forks of Bitcoin and Ethereum
For example, in August of 2017, Bitcoin (BTC) underwent a hard fork to extend its block limit as a solution to scalability issues.
A new cryptocurrency with new specifications, Bitcoin Cash (BCH), was created.
Ethereum Classic is also a cryptocurrency that was created as a result of a hard fork of Ethereum.