An upgrade to a blockchains underlying protocol (or set of programmable rules) that sometimes results in the chain splitting into two separate chains; one that runs the previous protocol and another that runs the new upgraded protocol.
There are two kinds of forks: Soft Fork and Hard Fork.
A soft fork is a software upgrade to the blockchain that does not result in the chain splitting as long as the upgrade is adopted by the majority of nodes on the network.
A hard fork occurs when miners are divided on which set of protocols to adopt in order to continue validating transactions. This results in a split in which one group of miners rejects the software upgrade and continues to validate transactions and add blocks to the chain according to the older set of protocols, while another group of miners upgrades their nodes software and begins validating transactions and adding blocks to a new chain according to the new set of protocols.
When a hard fork occurs, holders of the cryptocurrency from the old chain are granted cryptocurrencies from the new forked chain. However, miners must pick one chain to continue validating transactions for each node they are running.
Learn more about blockchain forks.