Originally a branch of the Mozilla SeaMonkey suite, Firefox's initial intentions were to avoid the bloat and feature creep of browsers at the time. Keeping in tune with the original Mozilla browser, Firefox was built with cross-platform functionality and extensibility in mind. The latter played a huge part in Firefox's success with the sheer number of browser extensions available for Firefox being staggering.
Five years after launch, Firefox has made a name for itself and earned a reputable position as the number two browser in the world. Only time will tell if Firefox has the staying power to remain on top (or close to the top), and whether or not Microsoft can out-gun Mozilla as the evolution of browsers continue. Given that the nature of the Internet is likely to be vastly different five or ten years from now, it's hard to say for certain if any software we use today will still be around.