Fork
Any situation where a blockchain has two competing versions, either briefly by accident or lastingly because the rules changed.
The most common kind is accidental and short-lived: two producers publish blocks at the same height within moments of each other, and the fork-choice rule resolves it within a block or two, discarding the loser. The second kind is deliberate, a change to the rules classified as a hard fork or a soft fork depending on whether old software still accepts the new blocks. A third and looser use of the word describes copying a project's source code to start a separate network, which involves no split of an existing chain at all. Which meaning applies is almost always clear from context, but the three are frequently confused in coverage.
In practice
Two miners finding a block at the same height creates a fork that lasts until the next block extends one branch and the other is orphaned.
The common misunderstanding
A fork does not automatically create a second coin; most forks are momentary accidents resolved in seconds, or upgrades that everyone adopts together.