Back in August of 2014, Microsoft announced they would be discontinuing support for older versions of Internet Explorer across a number of Windows versions by January 12, 2016. Over a year later, with only one week left before the cut-off date, millions of users have yet to upgrade.
The move by Microsoft appears to be an inspired push to shift users onto their new browser, Edge, which is included by default with Windows 10. However, the new browser's branding doesn't really distinguish it from the former Internet Explorer (a blue, lower-case "e" continues to serve as the logo for Edge), and most users aren't likely to realize there is a new browser in play for Microsoft. New features for Edge include a distraction-free reading mode, the ability to annotate web pages, as well as integration with Microsoft's voice assistant, Cortana.
Most home users shouldn't have too much trouble upgrading. Microsoft Edge and the latest versions of IE will work fine for most common needs. Enterprises running web apps or intranet sites standardized on older versions of IE are not so lucky, though. Reworking code of custom software to be compatible with Edge, or even the newest versions of IE is an expensive under-taking, and may not even be possible with some services.
In addressing these concerns, Microsoft points to Enterprise Mode of Internet Explorer 11, which offers better backwards compatibility for legacy applications that won't normally work with the latest versions of Microsoft's browsers. Enterprise Mode will continue to be supported through 2020, to give businesses time to find alternative, modern solutions.
Despite Microsoft's efforts, most Windows users have abandoned IE and Edge, with as many as 70% of them have turned to Google Chrome. Google has also announced the end of support for Chrome on Windows XP, Vista, and OS X versions 10.6, 10.7, and 10.8 effective April 2016.
Regardless, home users are advised to stay current with the latest version of their web-browser to continue receiving the latest security updates and patches.