What is a fork?

In order to understand a fork it is important to understand how blockchain works.
The situation in which a blockchain splits, permanently or temporarily, is called a fork. Forks can occur naturally while mining or intentionally. When two chains following the same protocols, temporarily have the same accumulated proof-of-work and both are considered valid, a fork occurs. Forks are made possible by the open-source framework, which allows copies and modifications to be made to the original blockchain.
Forks are commonly used in cryptocurrency for adding new features or to undo the effects of hacking or destructive bugs. Forks have been popular attempt to solve Bitcoin’s scalability issues, and many others!
Hard fork?
A hard fork is a protocol change, where the old software makes a new protocol adhering blocks invalid as it continues to enforce old protocols. In order to prevent a hard fork, all old softwares are required to upgrade to the new protocols.
Often times, if a group of people (i.e. miners, developers, etc.) become dissatisfied with the current protocol a fork will occur, with a new protocol. Users must agree to these new rules to use the newly forked currency.
The most notorious Bitcoin hard forks include, Bitcoin Cash and Bitcoin Gold.
Soft fork?
A soft fork occurs when new protocols recognise old blocks as valid, meaning it is backwards-compatible. Similar to a hard fork, a soft fork is also able to split the blockchain when old softwares consider new protocols invalid.
Soft forks that occurred on Bitcoin’s blockchain include, BIP66, which introduced signature validation and P2SH, which modified Bitcoin’s address formatting.
The open-source nature of blockchain allows forks to occur in order to make improvements to the existing currency or to change the protocol entirely. As cryptocurrency increases in popularity, more disagreements are likely to occur, and thus, more forks are likely in the future.