A fork is a change to a blockchain that alters the entire network and its rules or software. In a decentralized scenario like blockchain, developers, miners, and validators alike must reach a consensus to implement the upgrade. If the agreement on the update is reached, the chain goes on as usual. However, if some of the participants do not agree, the blockchain can be divided into two separate versions; the fork in this case will be the split.
The main categories of forks include soft forks and hard forks. A soft fork is a more gentle change that is still compatible with older versions of the software. The servers that do not get upgraded are not cut off from interacting with the network as long as they abide by the new guidelines.
Hard fork, on the other hand, is a much more drastic change. It splits the network into two in a permanent way because the newly imposed rules are not to be followed by the old version. One faction that has upgraded follows the new chain while another that has not stays with the original chain. This is the case with Bitcoin Cash (a fork of Bitcoin) or Ethereum Classic (from Ethereum) which are examples of hard forks that have resulted in new cryptocurrencies.
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The reasons for forks vary widely from bugs to be fixed, new features to be added, and differences over governance issues to be handled through changing the protocol design, etc. To put it in simple words, a fork means the community is taking the blockchain in a new direction.