The Linux Operating System is something of a misnomer. Linux-based computers actually run the GNU7 Operating System, the fruit of the Free Software Foundation's effort at rewriting Unix from scratch. Linux consists of merely the kernel, which is a relatively small but fundamental part of a working computer. The kernel acts as the nervous system of the computer, directly controlling hardware such as keyboards, disk drives, and even other computers on its network. It also controls how a computer divides its time and resources between programs that are running. Programs that want to interact with the hardware, such as by writing a file to the hard disk, must do so through the kernel. In Linux's case, the kernel polices the programs to prevent them from performing illegal operations that may jeopardize the system or violate the operations of other programs. Linux's technical success is gauged by the speed and effectiveness with which it performs this task.
Linux is a system because it provides a standard interface to the hardware of a computer. Since new standards are extremely difficult to develop and adapt, the interface was modelled after an established existing system, Unix. Unix was quite expensive at the time, and only ran on special workstation hardware, not on personal computers. Therefore, there was quite a niche for Linux, dubbed as ``Unix for PC's.''
Linux is an open system, progressing very much at the whim of its users/developers. When Torvalds put his kernel on the internet, he was astonished by the amount of attention it received by other developers. He had never planned on getting such a large response, or on the kernel growing into a fully-fledged operating system in so short a time. He had just been trying to run basic GNU programs on his home PC. The users were instrumental in defining the technology as an alternative operating system.