"Power in Firebending comes from the breathe, not the muscles. The breathe becomes energy in the body. The energy extends past your limbs and becomes fire!"

"His chi is blocked. Who did this too you?"
"One of them hit me with a couple quick jabs and I couldn't Earthbend, and I could hardly move."

There you have it. The benders' chi is used to control the elements. If their chi is cut off, they can't bend. The martial arts associated with each element is merely how they control the element, using their chi. Movements that can be linked to the basic nature of what each element is. Freely moving, hard to contain. That's Ba Gua(sp?), that's Airbending. Flowing with the world, using your own force against yourself(stick your hand flatly in a bucket of water, now slap it, notice a diffence?) That's Tai Chi, that's Waterbending. Forceful, aggressive, yet graceful, that's Northern Shaolin, that's Firebending. Strong, powerful, steadlong, that's Hung Gar, that's Earthbending. Different people have different levels of chi and differetn limits on their bending. But, through training a bender can hone their control and open up a world of new moves and attacks. Still, it's all tied to the martial arts movements. You can't "flick your wrist" and cause a tornado in Avatar, even if you're and Airbender, no more than you can crack your knuckles really fast and blow fire out your ears in Naruto. (There's a few exceptions, breathing fire or gusts of air aren't kung fu, but breating is essential in any physical activity)

There probably won't be any hyper detailed explaination, because since this is in a land existing in a time comperable to the English thinking they could cure psykosis by drilling holes in your head. Maybe if they fast forward a hundred years or so someone in the Avatar universe would know enough about the body to give an official explaination. Until then, well there you go.