A hard fork is a split of a particular blockchain.
Blockchains are constantly being developed. For example, protocols are being optimized to make transactions faster or to adjust the size of a block. These types of decisions always have advantages and disadvantages. Often not everyone agrees with an update either. In tech companies, management is responsible for making these kinds of decisions. They determine whether or not an update is made. A blockchain like Bitcoin has no management. The blockchain is decentralized so there is no single party that can make decisions about the future of this chain. Often in situations like this, the decision is voted on. If more than half of the developers support a decision, this becomes the new way a blockchain will continue to be developed.
Sometimes there is a large group that does not support the decision. In such a case, the group may decide to continue with a blockchain on their own, there is then a "fork" or split-off. Bitcoin cash and Ethereum classic were created this way.
With Bitcoin Cash, part of Bitcoin's supporters wanted to increase the block capacity that should make transactions faster. The other part did not want this and thereupon it was decided to hardcore. From this, Bitcoin Cash was born.
There are different sorts of forks. Hardforks are the most invasive because an entire blockchain is split off. With a soft fork, only rules are changed without otherwise changing much about the way a particular blockchain works.
A soft fork involves making blockchain rules more stringent. These are often not major changes that already fit within the existing rules. For example, Bitcoin initially had no limit on the size of a block until Bitcoin developers decided to make this rule stricter and reduce the block size to 1MB resulting in a softfork. This fit into the old rules because it was already allowed to have blocks of 1MB or smaller and so for this reason nothing else needed to change.
With a hardfork, opposite to a softfork, the rules within the protocol are relaxed. Therefore, these rules fall outside the old rules, creating a problem. If Bitcoin originally had a block size of 1MB and it was decided to make it without a limit, miners would have had to update all software and hardware to comply with the new rules. Because with this change the entire Bitcoin network would have to be shaken up and there would be uncertainty about its future, it was then decided to release a new currency - Bitcoin cash.
