GNU is a Unix-like operating system. That means it is a collection of many programs: applications, libraries, developer tools, even games. The development of GNU, started in January 1984, is known as the GNU Project. Many of the programs in GNU are released under the auspices of the GNU Project; those we call GNU packages.
The name “GNU” is a recursive acronym for “GNU's Not Unix.” “GNU” is pronounced g'noo, as one syllable, like saying “grew” but replacing the r with n.
The program in a Unix-like system that allocates machine resources and talks to the hardware is called the “kernel”. GNU is typically used with a kernel called Linux. This combination is the GNU/Linux operating system. GNU/Linux is used by millions, though many call it “Linux” by mistake.
GNU's own kernel, The Hurd, was started in 1990 (before Linux was started). Volunteers continue developing the Hurd because it is an interesting technical project.