What are html5 video players
Short answer
They let you use the new Video API for audio&video files in the browser.
Long answer
A few years ago the one and only solution was Flash to display videos on the Net. Flash has therefore a lot of good features by now but one has to admit it was totally wrong to relay on a third party plugin known for its security risks to do something as straightforward as display video content. The browsers start to be able to do it by themselves, but as usual with everything related to video, it’s not as simple as it looks but we have today the right tools in the box.
The Opera Developper website has a pretty nice intro you can check out if you’re new to this HTML5 Video thing!
Comparisons on the web
If you’re here for the comparison, you should immediately checkout these pages. They are the best resources I found online. If you stumble on anything better than that, please tell me.
A good and practical comparison chart. It is still regularly updated
http://praegnanz.de/html5video/
There’s another comparison here, but it’s suspect to being more partial as the authors produce their own player.
http://html5video.org/wiki/HTML5_Player_Comparison
What are the success factors of the various players?
All are doing 3 things. Wraping the HTML5 API, fallback if a format is not supported by a browser and deliver an API to control the player.
Universal
A player has to work on as many browsers / OS as possible and be able to read as many formats as possible.
Free and Open Source
No proprietary / closed course. Stay clean and live happily
Good Looking
Good look matters. Customizable and same looking flash player is a good point
Featureful
Playlists, audio support, subtitles and so on.
Accessibility
Keyboard access and such things are http://dev.opera.com/articles/more-accessible-html5-video-player/
Developper friendly
Easy to install with a good API to work with.
And we skip…
All the players who are closed source and no open licence. For example Codoplayer or Sublime Video are good, but not in this scope.
The list
I have not tested in depth each and every one. If you have comments or feedback, I welcome them 
MediaElement
Very good one. Apart from being free (MIT Licence) and offering a same-looking Flash player for compatibility, it deals with the API in a clever way (the flash player “speaks” the HTML5 Video API). It is sort of light and simple which is an advantage. It is bound to jQuery but that works well for me and works just fine everywhere.
Compared with other players, the downsides are the lack of HLS support and playlists (though implementing your own is kind of straightforwared).
Code: https://github.com/johndyer/mediaelement
Official site: http://mediaelementjs.com
FlowPlayer
Flowplayer comes with a Commercial licence, GPL requires that you not remove the Flowplayer logo visible on the player.
You can download a simple, immediately working set of files and they have a commercial delivery service as well.
They have a very good documentation with immediately working examples, offer to deliver over a free cdn which is useful for tests.
It Support HLS and offers Playlists and is as featureful as can be. A very good pick.
Code https://github.com/flowplayer/flowplayer
Corp http://flowplayer.org
Features https://flowplayer.org/player/
VideoJS
Provided under Apache2 Licence, VideoJS is a good solution with rich community contributions.
No HLS, playlists or keyboard controls, but easy to use and customize, does the job just fine.
corp http://www.videojs.com/
code https://github.com/videojs/video.js
LeanbackPlayer
This is a free as in beer player with a non-commercial license: GNU GPL v3 but the source code is not available.
No playlist, no HLS, no Keyboard control. There is no custom fallback flash solution but you may use one provided by another free solution.
There’s not a lot of documentation, so it’s not so easy to install and use.
Corp http://www.leanbackplayer.com
Docs http://www.leanbackplayer.com/player_documentation.html
Open Standard Media
http://mediafront.org
https://github.com/mediafront/osmplayer
+ Licence MIT
– No HLS
– no playlist
Strobe Media Playback
Open Source Media Framework
http://www.opensourcemediaframework.com/
http://sourceforge.net/projects/smp.adobe/
http://help.adobe.com/en_US/FMPSMP/Dev/WS3fd35e178bb08cb34f377935129f1474d5d-7fff.html
+ HLS
+ BSD Licence
Projekktor
JWPlayer
This one has a distributed version and to use the free version, you must compile it which is kind of complex for a simple video player.
The licence is not absolutely clear and the player has cool features like HLS and playlists.
Corp http://www.jwplayer.com/
Specs http://www.jwplayer.com/tech-specs/
Code https://github.com/ybian/jw-player
Kaltura
This is a major player coming from a large video solution. They were chosen by the wikimedia Foundation in 2012 for information about how “institutional” it can be. Also they have the html5video.org domain name which has the comparison chart, but is of course a bit oriented on their own product.
It is Free (GPL) and featureful, but I personally found it annoying to set up. The documentation dooesn’t offer a single clear example and the player is bound to the original Kaltura solution.
Code https://github.com/kaltura/mwEmbed
Corp http://player.kaltura.com/docs/
Final notes
Many times you need to download the Flex SDK to compile the Flash Player. Turns out the download link can be hard to find for old versions: http://www.adobe.com/devnet/flex/flex-sdk-download-all.html