Embedding media in HTML5
For many, HTML5 first entered their vocabulary when Apple refused to add support for Flash in their iOS devices. Flash had gained market dominance (some would argue market stranglehold) as the plugin of choice to serve up video through a web browser. However, rather than using Adobe's proprietary technology, Apple decided to rely on HTML5 instead to handle rich media rendering. While HTML5 was making good headway in this area anyway, Apple's public support of HTML5 gave it a major leg up and helped its media tools gain greater traction in the wider community.
As you might imagine, Internet Explorer 8 and lower versions don't support HTML5 video and audio. Most other modern browsers (Firefox 3.5+, Chrome 4+, Safari 4, Opera 10.5+, Internet Explorer 9+, iOS 3.2+, Opera Mobile 11+, Android 2.3+) handle it just fine.
Adding video and audio the HTML5 way
Video and audio in HTML5 is easy. The only real difficulty with HTML5 media used to be listing out alternate source formats...