HTML5 is a family of new technologies, enabling us to build rich web applications. Currently many applications are built around Flash or Silverlight, which provide rich graphics, and multimedia capabilities to web pages.
HTML5 is an open platform (free to create and run) which promises, not just exciting multimedia capabilities - but many other features (such as storage, geo-location, offline access etc) with which we can build applications which blur the lines between traditional desktop and web.
Browsers are more like operating systems now, in fact Google's Chrome OS is a an attempt to use the Chrome browser as a OS for running various web apps. These web apps could be anything from word processing, games, or even programming IDEs. HTML5 plays a crucial part in this.
Not just on modern browsers, modern OSs like the upcoming Windows 8, will be integrating HTML5 based apps in its desktop interface ('Metro').
Since HTML5 technologies are fairly new, it only works on latest version of browsers, like Chrome, IE-9, Firefox 4+, Safari, IOS browser (on the iPhone and iPad) Also the level of support varies with browser implementation.
I got interested in HTML5, when I worked on developing a game for Microsoft's Dev-Unplugged contest. The game was selected as one the finalist in the contest and showcased stunning graphics using the new <canvas> element in HTML5. What was previously done using Flash, is now possible completely using just HTML5 and JavaScript.
The game is titled "Magician: Fairy Rescue" - created by Brunda Merinal, and me.
Here is a short video of the game:
You can play this at: http://www.relfind.com/game/magician.html