There is no system but GNU, and Linux is one of its kernels. --RichardStallman
(That's a quote from the GNU website. Meant as a joke, of course).
"GNU/Linux" is the term used by the GnuProject and its supporters, in particular its founder and main activist RichardStallman, to refer to the UnixLike OperatingSystem that is more commonly known as the LinuxOperatingSystem or simply Linux.
Linux, the program written by LinusTorvalds and others, is a UnixLike kernel (see WhatIsaKernel), not a complete operating system. The GNU project was started in 1984 to develop a complete operating system based on FreeSoftware. By 1991, when Linux development started, the GNU project had produced most of the major components of this system, including a shell, a C library, and a C compiler. These components were adapted by LinusTorvalds and other early Linux developers to work with the Linux kernel, creating a completely functional operating system. Although the LinuxKernel is licensed under the GnuGeneralPublicLicense, it is not part of the GnuProject.
Because a large part of the operating system had been created under the aegis of the GNU project, Stallman and others argues that it is more appropriate to call the full system "GNU/Linux", while the kernel itself can be called "Linux". This is very important to the GNU project for the followering reason:
Calling the system GNU/Linux recognizes the role that our idealism played in building our community, and helps the public recognize the practical importance of these ideals. (From http://www.gnu.org/gnu/gnu-linux-faq.html).
Requests to call the system "GNU/Linux" have met with mixed success. A few distributions, most prominently DebianGnuLinux, call their systems "GNU/Linux". Some users and developers in the free software and open source software community follow this request, while others ignore or oppose it.
The corporate world, including most media outlets, do not--probably because the corporate world generally prefers the ideals of OpenSource (which is focused on practical benefit) over those of FreeSoftware (which is focused on individual freedom). However, some exceptions such as MySql, TrollTech?, and TraversalTechnology? do espouse FreeSoftware.
Some consider the term "operating system" to refer to only the kernel, while the programs running on top of it are simply utilities (regardless of the practical necessity and volume of such utilities). In this sense, the operating system is called Linux, and a LinuxDistribution is based on Linux with the addition of the GNU tools. On the other hand, both the name GNU and the name Linux are intentionally parallel to the name Unix, and in some sense the term "Unix" refers not only to the kernel, but also to the C library and user-land tools--both of which come from the GNU project in most GnuLinux distributions.
Some of the reasons people refer to the system as GNU/Linux are: