Linux started in 1991 when Linus Torvald wrote a Unix-like operating system from scratch using GNU tools (such as the compiler, command line programs and etc.). GNU was started by Richard Stallman as a project under the supervision of the Free Software Foundation (FSF).
Today, about 5% of the Linux source code originates from Linus. This is a significant contribution by a single individual because the source code of Linux is massive.
Linux is not Unix, although it captures most of the essence of Unix. Linux is not even POSIX (Portable Operating System Interface for Unix) compliant, although it is mostly compliant.
What makes Linux different from Unix and Windows is its license. Linux is released through the GNU GPLv2 (General Public License version 2). The full text of the license can be found at http://www.linux.org/info/gnu.html.
As a consequence of GPLv2, Linux is free in two ways. First, it is free as in free of charge. Anyone can download the compiled binary or source code and compile it using GNU (also GPLed) tools. Second, it is free as in freedom. The license specifically permits modifications to the source code. The modified versions automatically inherit GPLv2.
This “viral” nature of GPLv2 makes Linux the perfect platform for experimentation, research and specialization. Anyone can take a specialized version and add to it. Linux is widely used in academic (e.g., universities), research (e.g., national labs) and commercial (e.g., router manufacturers) organizations. The total number of developers contributing to Linux is in the order of thousands.
Even though many manufacturers used to own and maintain their own Unix operating systems, some have switched to use Linux instead. Most notably, IBM started to use Linux in 2001, and nearly recouped its investment in one year. HP (Hewlett Packard) also switched at about the same time for their servers.
Although Linux is mostly known as a server OS, it is increasingly accepted as an alternative desktop OS.