Firefox added MP4/H.264 Video Support
Firefox for Android now supports HTML5 based H.264 video playback. According to Mozilla, Firefox currently supports H.264 playback on any device running Android 4.1 (Jelly Bean) and any Samsung device running Android 4.0 (Ice Cream Sandwich).
Android 4/4.1: hardware and software decoder support for h.264 video
See details here: https://www.mozilla.org/en-US/mobile/17.0/releasenotes/
To test whether your Firefox supports H.264 on a compatible device, try playing this MP4/H.264 video.
The HTML5 video element was supposed to offer a standards-based way to play online videos without proprietary plugins such as Flash or Silverlight. Unfortunately the web ended up with proprietary video codecs, see HTML5 video formats and codec. The codec war has created a split in browser support for HTML5 video, see HTML5 Video Browser Compatibility.
Firefox previously refused to support H.264, citing royalty and licensing concerns. Now it seems they have abandoned the fight against H.264 in HTML5 video
H.264 support for older Gingerbread and Honeycomb Android devices is still in the works. At the same time Mozilla is adding H.264 support to desktop Firefox as well.