What is a hard fork?
With a hard fork, the blockchain is changed so strongly that it is no longer downward compatible from the time of the fork. In order to change the protocol of a blockchain, there must be a consensus among all network participants and thus an update of the software. If the participants do not agree, so that there is no consensus, the blockchain branches off. Both possibilities (with and without consensus) correspond to a hard fork. A well-known example for a split without consensus of the participants is Bitcoin Cash from the year 2017.