The GNU Operating System
The GNU Operating System is a OS which was launched as a project codenamed "The GNU Project" in 1984. It's goal was to develop a complete UNIX-like operating system which is free software. The good people involved in GNU managed to piece together a complete OS - except for one important piece: The kernel.
 The name
Some guy in Finland developed a kernel which happened to fit very well into the GNU Operating System. This kernel was eventually named "Linux".
The corporate media realized that the GNU people are all about freedom - and "Free software" - in a matter of liberty, not price. They also realized that the guy from Finland wasn't promoting freedom and ethics anywhere near as the GNU people, so they soon decided to only use the name "Linux" when they - rarely - mentioned the "The GNU Operating System".
 Available variants
Variants of The GNU Operating System who use the Linux kernel are known as Linux distribution. There are dozens and dozens of slightly different Linux-based GNU distributions available, but they are all based on very similar concepts. There are also variants of the The GNU Operating System who use other kernels.