Video on the web is a mess. Web standards have never fully embraced video. Until HTML5, there was no video element, so the only way to play video was to depend on platform-specific software. HTML5 provides a video element, but you're going to need to provide video in multiple formats.
At its purest, the HTML5 video tag is a very simple. To deliver video that plays in Firefox and Safari, however, requires two different video formats, and you still need Flash for IE. Here's the code to make it happen.
HTML5 includes a handful of new structural elements that are designed to make markup more meaningful. You can use these elements today; they don't really do much, so browsers don't need to explicitly support them. And it takes only a little trickery to make them work even in IE.
Video is becoming more and more popular as an element of web pages. With the fragmented technology standards, providing video that plays everywhere can be tricky. Fortunately, there's an assortment of solutions available that package up all the complexity and provide a single, integrate solution for video that just works.
An excellent book on HTML5, available online or in print.