The code for most cryptocurrencies is open-source, and the community operates by consensus, so sometimes newly modified code is released that is adopted by some, creating what’s called a fork.
A Bitcoin Fork is when the blockchain, made up of interconnected computers holding a distributed and permanent record of all bitcoin transactions up to that point, is offered a modified currency protocol that is adopted by some of the Bitcoin community, which creates a “fork” in the previously longitudinal history of the ledger (i.e. “a fork in the road”), where one ledger continues to grow based on the changed protocol, and one ledger continues to grow with the old protocol still intact.
The newly created protocol is a new version of the bitcoin currency, and so it is given a new name, such as Bitcoin Unlimited, or the most recent fork, Bitcoin Cash. Sometimes this causes the older protocol to take on a new moniker to distinguish itself from the new fork. When the new currency is created, generally the holders of the old currency are instantly credited with an equal balance in the new currency, since the bitcoin code that they own is now the link between the old chain and the new fork.
They can move forward with both balances, although the new currency will have a completely different value than the old currency, and, like a stock split, the value of the old version may deplete some in the near term, as some will sell off their old currency in favor of buying the new one at a low price (if they believe it will be successful). Some forks don’t go anywhere, and the nodes that attempted to implement the fork will eventually go back to the old version and become part of the main blockchain again.
This can even occur when the new protocol is a completely different animal, the way litecoin is considered a fork but it did not compete with bitcoin itself. Forks are sometimes delineated into specific varieties, such as hard forks, soft forks, and, in the cash of the altcoin “dash,” sporks, but given the ever-changing nature of the technology and terminology, and in the interest of keeping things simple, we’ll just leave it at that for now.