A fork is an independent copy of a codebase or repository, created so that work can proceed on it without affecting the original.
The everyday sense belongs to hosted version control. On 📝GitHub, forking makes a server-side copy under your own account and is the standard first move in contributing to someone else's project: fork, branch, change, open a pull request back upstream. It is low-stakes and expected to reconverge — the copy exists to be merged, not to persist.
The older open-source sense is a governance event rather than a workflow step. A project forks when contributors disagree irreconcilably about direction, licensing, or leadership, and the new line is meant to diverge permanently. LibreOffice split from OpenOffice, MariaDB from MySQL, and io.js from Node.js, the last of which reconverged after the dispute was resolved. Permissive licensing is what makes this possible at all, and the credible threat of it is a real part of what keeps open-source maintainers accountable to the people building on their work.
The word also names an unrelated systems concept — fork(), the call that creates a child process by duplicating the parent. Same metaphor of a path splitting, entirely different subject; worth keeping the two apart in conversation.