The GNU project is an effort to create an entirely open-source Unix-like operating system, and is still considered to be in active development, although the first version of the kernel, GNU Hurd, has yet to be released. The GNU project has lent its name to a variety of open-source licenses designed for use by the project, the most famous of which is, perhaps, the GNU Public License.
GNU is a recursive backronym for the phrase "GNU's Not Unix".
As GNU's kernel is yet to receive a stable release, the GNU tools are mostly used with the Linux kernel, resulting in a GNU/Linux operating system. Nearly all well-known Linux distributions are GNU/Linux OSes, though exceptions exist (for example, Debian has a GNU/kFreeBSD version, while Android uses the Linux kernel with BSD tools).