In this case "Biting Hard" is a hash tag on twitter. It has no relevance or meaning to the picture. Even as a hash-tag I cannot see any meaning other than the obvious one of biting on food. It might be some kind of American slang or may just be a collective name for things which look funny or are ironic. Either way, there is no formal or informal meaning. I'm sure its slang or "ghetto speak".

You know, I've been thinking about what I've heard people say instead of "bite hard," and I feel like at least here, "jack my style" (http://www.italki.com/question/231214) or "crimp/cramp my style" (http://www.ditchwalk.com/2010/11/22/to-crimp-or-to-cramp/) are much more common. Are these common in the UK as well? I don't recall saying any of these myself, except perhaps "jack my style" when I'm singing along to the fun. song :~) https://www.youtube.com/watch?v=qQkBeOisNM0