The GNU project were early promoters of open source operating systems and software. It launched in 1984 to develop the GNU operating system, a complete Unix-like operating system which is free software. That is software which respects your freedom as well as being open source.
GNU has rewritten several Unix-tools under a free license. What we commonly refer to as Linux or "GNU/Linux" is actual the Kernel (Linux) plus the GNU Utilities like bash plus other open source software.What is known as Linux could most accurately be called GNU/Linux. That is the GNU tools with the Linux kernel. GNU are also developing their own kernel called Hurd.