Last week, there were a couple of big developments for HTML5, both YouTube and Vimeo implemented HTML5-based video players on their sites. This is a huge step forward for the proposed standard, but most users won't be able to take advantage of it. Right now, the players only work on recent builds of either Google Chrome or Safari leaving out the bulk internet users which either use Internet Explorer or Firefox.
IE doesn't support HTML5, and doesn't plan to in the short term future, but IE users can get around that by installing Chrome Frame. It's not an ideal solution, but it will get you HTML5 videos. Though, if you care about that, you're probably not using IE anyway.
Firefox, on the other hand, has great support for HTML5, including the <video> component. In fact, some of the current limitations in the HTML5 video players, i.e. no full-screen video, wouldn't be a problem on Firefox which supports the feature, unlike Safari or Chrome. So why then is Firefox left out of HTML5 video party? It doesn't have anything to do with the technology the problem is with the proprietary codec both video sites use and which Mozilla doesn't support.
Both YouTube and Vimeo use the h.264 codec for the videos streamed with their HTML5 players. They argue it offers better flexibility and quality at this point over open alternatives, which may very well be true. Vimeo said it best:
"Almost every thread on the internet about HTML5 devolves into some kind of flamewar. Please don't comment here extolling the virtues of open source or unencumbered codecs. We know, it's our job to know, and that conversation has been had a million times... The simple fact is right now h264 allows us the most flexibility to display on many devices and many players with the same file. When that changes, so will we."
Technically, most people would agree that h.264 is better for streaming video than Theora, the open alternative, though the latter is making progress and is comparable in many examples in both quality and bandwidth consumption. But there are other reasons behind Mozilla's decision, about which you can read here, and they don't have much to do with the technical aspects of the issue.