Linux is a free Unix-type operating system kernel originally created by Linus Torvalds with the assistance of developers around the world. Developed under the GNU General Public License, the source code for Linux is freely available to everyone. Because of its robustness and availability, Linux has won popularity in the open source community and among commercial application developers.
There are versions of Linux for almost every available type of computer hardware from desktop machines to IBM mainframes. This has resulted in thousands of people working on various aspects of Linux and adaptation of Linux for a huge variety of purposes, from servers to TV-recording boxes.
Linux refers to a specific operating system kernel. The entire "free" operating system is correctly referred to as "GNU/Linux", which refers to both the kernel and all of the tools developed over a 15-year period by Richard Stallman and Project GNU.
(very incomplete defintion, needs links and more meat)