Despite being a world organisation of “open source,” Mozilla clearly does not like H.264 which is open-source itself. Although H.264 is also free, the licensing says that it might not be free in the future (which I highly doubt so), but certain open-source extremists wouldn't have missed this point to bash Apple.
There was the free Ogg Theora video codec Mozilla (and many Mozilla followers) enjoyed and decided to use that format to fight against H.264. Apart from within certain extreme groups, Ogg Theora did not get well adopted.
Then, there's WebM from Mozilla's long time major financial supporter - Google.
Mozilla even tried to convince major video sites (apart from Google's YouTube) to switch to WebM. They declined. This made Firefox (and Gecko browsers) the only mainstream browser that does not support H.264.
H.264 is open-source, not an Apple technology. Except a number of open-source extremists automatically associates H.264 to Apple.