A long long time ago (in computer science terms, that translates to 26 years) the Mosaic web browser was developed at the National Center for Supercomputing Applications, University of Illinois - Urbana-Champaign.
Soon mosaic became Netscape communicator and became among the most successful web browsers. However this was not to stay with Microsoft upsetting the bandwagon with their free Internet Explorer ( a.k.a. Internut Exploder in the anti-microsoft circles; in fact, wikipedia redirects Internut Exploder to Internet Explorer :D ) which was bundled along with the Windows operating system.
The United States vs. Microsoft lawsuit was settled mostly in favor of microsoft. Pursuant to AOL takeover of Netscape, the Mozilla Foundation, which had already been set up as a subsidiary of Netscape, was made a separate entity.
And Mozilla made the Mozilla application suite which today goes by the name Mozilla SeaMonkey. Some of the brilliant intellectuals at Mozilla soon decided that commercial requirements have resulted in a drastic feature creep into Mozilla, bloating up the application suite. Hence, Firefox was spun off as an experimental branch to combat this.
Firefox version 1.0 was released on November 9, 2004. Since then, it's adoption by the market has been dramatic.
Today, Mozilla firefox holds a whopping 21.1 % of the global browser market share.. A place which was dominated by over 90% by the Microsoft Internet Explorer !!!
Way to go!!
On a subtler note, what will become of the GNU IceWeasel vs Mozilla Firefox, is another question only time can tell though.