I don't believe that OSX or Linux provide it, which is why Firefox does not support it natively. Hopefully this means that they've finally worked out an agreement for licensing, and can support it.
Support H.264/AAC/MP3 video/audio playback on desktop Firefox (https://bugzilla.mozilla.org/show_bug.cgi?id=799318)
On Linux Firefox will use GStreamer, the same backend also used in Firefox OS, its not enabled in the nightly builds since not all distros have the right version of GStreamer and it ca not be loaded dynamically right now (https://bugzilla.mozilla.org/show_bug.cgi?id=794282)
For OS X the plan seams to be to use AV Foundations but no patch has been submitted so far. (https://bugzilla.mozilla.org/show_bug.cgi?id=801521)
In fact, there's this bug for H.264 support: https://bugzilla.mozilla.org/show_bug.cgi?id=541286
It was raised in January, and it's status is: "RESOLVED WONTFIX"
The stable Firefox build, as of today(12/19/2012) does not support those codecs.
- support for Linux via GStreamer landed but not built by default. It needs a bit more work.
- support for Windows 7 and above which the OP post is about
- Mac OS X is not yet underway but is planned.
- Hardware H.264 decoding on Android phones via libstagefright. Some phones supported and enabled by default. Some supported but disabled at the moment. Some unsupported.
- Hardware H.264 decoding on Firefox OS/B2G enabled by default, implemented via libstagefright. Phone vendors provide the binary blobs to do the decoding.
For detection sites should use the API "canPlayType" and similar functionality to detect if the browser supports playback.
EDIT: Well, I'll eat my hat. I'm not sure why Firefox needs a different licensing agreement on OSX when they COULD just hook into quicktime without any licensing fees at all. I'm probably grossly misunderstanding the situation.
EDIT2: Ok, so I guess AVFoundation is just the objective-c frontend for OSX's media libs. I can't for the life of me understand why it took them so long to implement.