Software Libre Foundation
The GNU/Linux operating system is the operating system that is more commonly referred to as Linux. The "Linux" in GNU/Linux is the kernel of the operating system. The GNU part comprises the user tools and general other software due to which GNU/Linux can claim itself to be a complete operating system as defined in the Open Group's POSIX standard.
To make an analogy; The Linux kernel would be the engine of a car ie. the central part that drives everything else, the GNU part would provide everything that makes an engine usable to get from A to B.
GNU is a project established in 1984 with the purpose of revising the current course the software industry was heading for.
To accomplish this they published a license known as the GNU General public license (GNU GPL).
The goal of the GNU project was to establish a complete operating system (including a kernel), that could be distributed under the GNU GPL. Around 1992 this operating systen was a reality, if not for one central part; the kernel.
A little earlier, Linus Torvalds had released his kernel on the internet licensed under the GNU GPL, enabling many programmers to adopt and improve and republish it.
Meanwhile development of the kernel for the GNU project had already been started, but the state of the Linux kernel was already more advanced. The Linux kernel had been adopted by many programmers and matured rapidly, as the design for the GNU project's native kernel was complicated. It was a natural step to use the Linux kernel as the driving part of the GNU operating system, leading to a complete operating system called GNU/Linux .