The GNU project was launched in September 1983 by Richard M. Stallman to create a complete operating system which is Free Software. Software development work started the following January. Today we have several Free Software operating systems which respect the users' freedom by giving everybody the right to use, study, share, and improve the software for any purpose.
Stallman established the Free Software Foundation in October 1985 to assist administrative, legal, and organisational aspects of the GNU project and also to spread the use and knowledge of Free Software. The main licences of the GNU project are the GNU General Public License (GPL) and the GNU Lesser General Public License (LGPL, originally called GNU Library General Public License). Over the years they have become established as the most widely used licences for Free Software.
The GNU project consists of numerous smaller sub-projects maintained by volunteers or businesses or combinations of the two. These sub-projects themselves are also called "GNU projects" or "GNU packages."
The name of the GNU project is derived from the recursive acronym "GNU's Not Unix." Unix was a very popular operating system in the 80s, so Stallman designed GNU to be mostly compatible with Unix so that it would be convenient for people to migrate to GNU. The name acknowledges that GNU learned from Unix's technical design, but also importantly notes that they are unrelated. Unlike Unix, GNU is Free Software.
Being Unix-like, GNU is modular in design. This means that third party components can be inserted into GNU. Today, it is very common for people to use a third party kernel called Linux with GNU systems. Many people use the name "Linux" for this variant of GNU, but this prevents people from hearing of the GNU project and its goal of software freedom. FSFE asks people to use the term "GNU/Linux" or "GNU+Linux" when refering to such systems.