A fork occurs when the single blockchain splits into two, either due to:

A split in consensus among the miners and engineers that maintain the decentralized network or
A change in the underlying rules of the protocol of the blockchain that is accepted by the persons who oversee the network.
A change in the underlying rules of the protocol is generally classified into 2 broad categories: soft forks and hard forks.

Soft Forks & Hard Forks
A soft fork is a software upgrade that is backwards compatible with older versions. This means that participants that did not upgrade to the new software will still be able to participate in validating and verifying transactions. Soft forks represent a gradual upgrading mechanism as those who have yet to upgrade their software are incentivized to do so, or risk having reduced functionalities.

Hard forks refer to a software upgrade that isn’t compatible with older versions. All participants must upgrade to the new software to continue participating and validating new transactions. Those who don’t upgrade are separated from the network and unable to validate the new transactions. This separation results in a permanent divergence of the blockchain. As long as there is support for the minority chain, in the form of participants mining in the chain, the two chains will concurrently exist.

Bitcoin’s Forks
Litecoin, Dash, Bitcoin Cash, Bitcoin Gold among others were all founded under the premise of improving the Bitcoin protocol in terms of transaction times, transaction costs, mining characteristics etc.