If you use the site's HTML5 player without Media Source Extensions, only some video resolutions are made available. In particular, 720p is the highest quality that is available in this case even if the video itself is also available in 1080p or even 4k.
Note: This is not the case if Adobe Flash is used to play videos on YouTube.
Other sites and services, Netflix for instance, have also started to make use of it but not to the extent that it is used on the YouTube video hosting site.
You can check if your browser supports MSE by visiting YouTube's HTML5 Video Player page. If you are using any version of Firefox except Firefox Nightly you will notice that all three Media Source Extension checks fail in the browser.
Other browsers, Google Chrome on all platforms or Internet Explorer on Windows 8 or newer support Media Source Extensions either completely or at least partially.
Mozilla has been working on integrating Media Source Extensions in Firefox for quite some time. The Nightly version of the web browser supports Media Source Extensions since May 2014 and while development has not been completed yet on the integration, it works well for the most part.
Up until now you had to change a parameter in Firefox's advanced configuration to enable support for MSE in the browser. This was done by setting the parameter media.mediasource.enabled to true.
This has changed with the most recent Nightly update as the parameter's default value is true now. What this means is that MSE is now supported by Firefox Nightly without the user having to do anything for that anymore.
While that is the case, it is unlikely that Firefox 36 will be the first stable version of Firefox to support Media Source Extensions. As mentioned earlier, development is not complete yet and Mozilla plans to disable the feature before the stable channel hits version 36.
Firefox users who notice issues when using video streaming services may want to consider turning off Media Source Extensions in the browser to see if that resolves the issues. All that needs to be done for that is to set the parameter above to false. (via Sören)
Update: Mozilla introduced two new parameters recently that handle Mp4 and WebM support in Media Source Extensions. For full support, make sure that the parameters media.mediasource.mp4.enabled and media.mediasource.webm.enabled are set to true in Firefox.
As their names suggest, these two parameters define whether support for webm or mp4 is enabled or not in Firefox when Media Source Extensions are used.
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