Recursive Acronym for GNU's Not Unix, a project working on the GNU OperatingSystem.
They are making a Kernel called TheHurd and a set of UserSpace utilities.
Because the Kernel and UserSpace utilities are individually exchangable, RMS want Linux distributions referred to as GNU/Linux, reasoning that they use mostly GNU UserSpace utilities. While they use the Linux Kernel, a similar OperatingSystem could just as well use a different one and still be composed mostly of GNU UserSpace utilities, such as GNU/Hurd. However, strangely, while the glibc, sysvinit, and a number of other crucial system components were made by the GNU project, the question of whether the majority of UserSpace is under a GNU license (GPL/LGPL) or 
some other license doesn't appear to enter into this dicussion.
-- This description is pretty poor and inaccurate; especially for a crucial part of the GNU/Linux operating system.
The GNU Project was founded by RichardStallman (RMS) in 1984 to create a Free operating system called GNU (which stands for GNU's Not Unix). GNU is based on the UNIX design, however it does not strictly follow it; its developers often improve on the original Unix designs. The GNU Project's goal is to create a complete, Free operating system, not just a simple kernel capable of running applications.
Development on the GNU system started in userspace software; in order to have free operating system; you needed a free toolchain (compilers, linkers, assemblers etc.) and development began on those parts of the system. This approach had the benefit of being able to develop, test and run the programs on existing Unix systems; which helped to ensure all of the software could be used as a drop in replacement for existing Unix software (where neccessary).
By about 1990; most of the operating system was developed, short of a decent kernel (they had small, crude kernels they used for development but nothing stable). The GNU project developers were waiting for Mach to be released as free software before they started working on the GNU kernel TheHurd which was a collection of servers that ran over the Mach microkernel to provide a Unix like kernel.
Further delays with Mach and technical problems debugging Hurd set development back severely. In the meantime, Linus Torvalds started developing a small Unix-like kernel called "Linux" with the intention of making an operating system. (Linus took an opposite approach to the GNU project by starting on the kernel). The Linux community began making Linux versions of GNU packages, and it took a while before any real cooperation took place in combining GNU and Linux (possibly due to poor communication etc.) With a little bit of glue; Linux (the kernel) filled the gap in the GNU system and allowed people to run a complete free operating system.
The GNU Project requests the operating system is called GNU/Linux as opposed to Linux (or just GNU); to quote the 
GNU/Linux FAQ:
"Most operating system distributions based on Linux as kernel are basically modified versions of the GNU operating system. We began developing GNU in 1984, years before Linus Torvalds started to write his kernel. Our goal was to develop a complete free operating system. Of course, we did not develop all the parts ourselves--but we led the way. We developed most of the central components, forming the largest single contribution to the whole system. The basic vision was ours too.
In fairness, we ought to get at least equal mention"
See also:
60 pages link to GNU:
