The video I have chosen to embed here is Big Buck Bunny, a short movie created by the Blender Foundation both to provide free and open films and games and to improve the Blender software used to create the movie.  I embedded this video primarily because Big Buck Bunny was released under the Creative Commons Attribution License, which dramatically reduces the copyright issues associated with me embedding it.  This is important because if I chose any video I'd like for this page, I would be setting myself and the school up for a copyright lawsuit.  Perhaps this is why many web sites use this for testing their video players.

As for the player, it is quite a work.  This web page itself does not contain any <video> or <object> tags, rather it contains a <div> tag containing a video player which is dynamically generated on the web page.  In order to ensure compatibility across a wide range of browsers, a JavaScript function places the video either in a <video> tag, or if the browser doesn't support HTML5 video, a Flash player inside an <object> tag.  The video container also allows for multiple, comma-seperated files for the video player; in this case, that includes a WebM version for Firefox, Chrome, and Opera, and a H.264 MPEG4 version for Safari, newer versions of Internet Explorer, and the fallback Flash player (which is used primarily by older versions of Internet Explorer, which don't support HTML5 video at all).