A Fork is an event that signifies the separation of any one (or possibly more) Cryptocurrency. During a Fork, a Cryptocurrency can be split into 2,3 or more separate Cryptocurrency entities, depending on the circumstances.
Hypothetically, such separations could take place due to a myriad of factors. They also tend to be highly contentious in nature which is often the cause for the emergence of seperate entities.
The most commonly seen type of Fork occurs when a proposed upgrade to a Cryptocurrency does not reach a 100% consensus from the community. A small percentage of the community does not adopt the changes to the network. They would break off from the majority and function on either Old or Separate but new set of rules. This is illustrated below.
New Protocols Fork
Separate Protocols Fork