When Netscape Navigator first hit the scene back in 1994 it marked the beginning of the Internet as a viable, useful and, for the first time, easily accessible service. A few years later Microsoft released Internet Explorer and many people at the time thought that Microsoft had already missed the Internet boat.
In the years that followed Netscape and Explorer battled it out for adoption and ultimately dominance of the browser market. Admittedly Microsoft had the resources to essentially buy the market rather than win it with a more robust product (plus they were giving it away for free while Netscape continued to build profits through direct sales). But even though Netscape charged for the product in the mid to late 90's they were the clear winners in terms of browser usage holding an estimated 90% of the market
But Netscape began to run into problems – not from competition with Microsoft, rather through a series of different owners, buggy releases, an increasing rise of security threats and plug-in compatibility issues. By the end of the 90’s Netscape had slipped from outright ownership of the browser market to barely clinging to a 4% market share.
Microsoft Explorer didn’t so much win the browser wars – Netscape just morphed into something different – something that wasn’t completion anymore.
From the late 90’s to the mid 2000’s Explorer was the dominate browser that everyone crazy enough to try and compete with them would copy. But a few competitors like Mozilla (basically a variation of Netscape) and Firefox did begin to gain traction (although many people chose to use these browsers specifically because they weren’t Microsoft Internet Explorer, not necessarily because they were better browsers).
Meanwhile in 2003-4 Apple began pushing their own web browser Safari. Up until that time Macs shipped with both IE and Navigator.
In the mid to late 2000’s mobile devices began to claim more and more of the online surfing time that people spent and a host of lightweight, proprietary browsers began to crop up.
Then in 2008 Google released their Chrome browser. As of July 2014 it is estimated that Google Chrome has a 45% share of the browser market so it is now the most widely used web browser in the world.
It hasn’t helped that Microsoft sort of abandoned IE and 2014 has been a terrible year for the browser particularly due to security issues. When the experts advised people to stop using IE until the security problems had been fixed that pretty much put the last nails in the coffin.
People started using one of the other alternatives and began to realize that browsers like Chrome, Safari or Silk or whatever were just as good, if not better than IE and even after Microsoft fixed the problems people aren’t coming back. If they had contiued to invest in Explorer over the years they may have been able to maintain their hold, but they've let the browser market slip through their fingers.
Microsoft will probably continue to support Explorer and they will probably try to make incremental improvements, but their time in the spotlight has passed and it’s unlikely that they will ever regain dominance in the browser market again.