Blockchain forks are essentially a split in the blockchain network. The network is an open source software, and the code is freely available. This means that anyone can propose improvements and change the code. The option to experiment on open source software is a fundamental part of cryptocurrencies, and also facilitates software updates to the blockchain
Forks occur when the software of different miners become misaligned. It's up to miners to decide which blockchain to continue using. If there isn't an unanimous decision, then this can result in the creation of two versions of the blockchain. There can be periods of increased price volatility around such events.
Forks work by introducing changes to the software protocol of the blockchain. They are often associated with the creation of new tokens. The main ways of creating new cryptocurrencies are to create then from scratch. Or, to fork existing cryptocurrency blockchain.
Creating new tokens from scratch is the most common method. This method involves the copying and pasting of existing code, which is then modified and launched as a new token. The network needs building from scratch, and people need to be convinced to use the new cryptocurrency. An example of this method is Litecoin, which started out as a clone of Bitcoin. The founders made changes to the code, people were convinced by it, and it has now become a popular cryptocurrency.
The alternative method is to fork the existing blockchain. With this method, changes are made to the existing blockchain rather than starting from scratch. In this case, two versions of the blockchain are created as the network splits. An example of this can be seen with the creation of Bitcoin Cash. Differing opinions around the future of Bitcoin led to the creation of a new cryptocurrency from the original cryptocurrency.