In the open-source community, a fork is what occurs when two (or more) versions of a software package's source code are being developed in parallel which once shared a common code base, and these multiple versions of the source code have irreconcilable differences between them. This should not be confused with a development branch, which may later be folded back into the original source code base. Nor should it be confused with what happens when a new distribution of Linux or some other distribution is created, because that largely assembles pieces than can and will be used in other distributions without conflict.
Forking is uncommon; in fact, it is so uncommon that individual instances loom large in hacker folklore. Notable in this class were the http://www.xemacs.org/About/XEmacsVsGNUemacs.html, the GCC/EGCS fork (later healed by a merger) and the forks among the FreeBSD, NetBSD, and OpenBSD operating systems.