The W3C organization (World Wide Web Consortium, the main international standard organization for the WWW) defines it in the specs simply as “the 5th major revision of the core language of the World Wide Web: the Hypertext Markup Language (HTML).”
A brief history
But HTML5 is not one big thing; it is a collection of individual features, like canvas, video, or geolocation, due to its complicated history that is detailed in a great post from Robert Nyman.
Basically, after 1998 when the HTML4 specification was published, the W3C membership decided to stop evolving HTML and instead begin work on an XML-based equivalent, called XHTML. This effort started with a reformulation of HTML4 in XML, known as XHTML 1.0 in year 2000).
But support for it was not wide-spread among the browsers (mostly because of the draconian error handling) so adoption by web authors and developers was very slow and eventually (when the W3C was working on an XHTML2, not intended to be backward compatible) Apple, Mozilla, and Opera jointly announced their intent to continue working on the HTML effort under the umbrella of a new venue called the WHATWG (this was 2004).
This effort produced the HTML5 draft specifications which were so successful to induce the W3C to revise their decision and from 2007 to start working together with the WHATWG and publish the HTML5 specs under its copyright.
In July 2009, the W3C announced that the XHTML2 charter will not be renewed. XHTML is dead, long life to HTML5.
A timeline is published on the W3C wiki.
HTML5 new semantic elements and APIs
HTML5 introduces several new elements: video, canvas, geolocation, local storage and more. And new APIs as microdata and drag-and-drop interfaces. I plan to visit them in a series of posts.
More and more browsers are supporting the different HTML5 elements (video, canvas and geolocation the ones with the widest support). Here is a table summarizing in which browser any HTML5 element is available.