Back almost ten years ago, Google came out with a tool named Google Webmaster Tools and since then it has grown tremendously.
Today, Google announced the tool will be renamed to Google Search Console as to not limit the audience to webmasters.
Google said the tool is not just for webmasters but also used by hobbyists, small business owners, SEO experts, marketers, programmers, designers, app developers, and, of course, webmasters as well. So they didn't want the name to limit the reach.
Because of that, Google has renamed the tool to Google Search Console.
They also made a short URL named http://g.co/SearchConsole but the end point URL still goes to google.com/webmasters. Not sure if that will change.
Google's John Mueller reminisces on Google+:
I remember ... back when Google Webmaster Tools first launched as a way of submitting sitemap files. It's had an awesome run, the teams have brought it a long way over the years. It turns out that the traditional idea of the “webmaster” reflects only some of you. We have all kinds of Webmaster Tools fans: hobbyists, small business owners, SEO experts, marketers, programmers, designers, app developers, and, of course, webmasters as well. So, to make sure that our product includes everyone who cares about Search, we've decided to rebrand Google Webmaster Tools as Google Search Console.
Functionality, no changes announced with this renaming but they are always pushing out new features.
Forum discussion at Google+.