A fork means applying changes, according to which the blocks are validated, to a blockchain’s program code.
After a soft fork, the new blocks of transactions are changed without rewriting the very rules of forming the chains of blocks. The network’s nodes running on the old software will still consider new transactions valid; hence, the integrity of the chain of blocks that include transactions will not be violated.
A hard fork implies changing the very consensus algorithm by splitting the network into two incompatible parts. This happens since blocks validated in one of the parts will not be validated in the other. Thus, once a hard fork occurs, it is mandatory that all users or nodes update to the latest version of a protocol software.
The most popular cryptocurrencies that emerged from the Bitcoin network’s hard forks are Bitcoin Cash and Litecoin; as for the Ethereum network, it is Ethereum Classic.