Both films depict a dystopian future where humans control either robotic or biological replacement bodies from afar. Although such technology is currently more science-fiction than reality, DARPA is determined to spend $7 million (in 2013) from its $2.8 billion budget to move the US military closer to an Avatar-like future.
While the project is officially titled "Avatar," DARPA obviously has little interest in creating a race of blue-skinned aliens, but rather, a bipedal robot that can be controlled using telepresence and other technologies to replace an actual live soldier on the battlefield.
DARPA's description for the program (cited by Wired Dangeroom) reads, "the Avatar program will develop interfaces and algorithms to enable a soldier to effectively partner with a semi-autonomous bi-pedal machine and allow it to act as the soldier’s surrogate."
DARPA envisions such robots as being agile and smart enough to execute potentially dangerous ops such as "room clearing, center control, and combat casualty recovery." It should be noted that the Pentagon has a long history of investing heavily in autonomous robot systems, like the AlphaDog, which is designed to carry equipment for soldiers in the field.
As expected, DARPA is seeking partners to work on its Avatar project and wants to develop "key advancements in telepresence remote operation of the ground system." At its core, it seems like DARPA is interested in a robotic soldier that can be controlled remotely by a soldier more intuitively than using something like a joystick.
Still, I honestly don't understand why DARPA specifically wants bipedal robots. I would think a wheeled or tracked robot could be better in certain situations and at least somewhat easier to develop.