This is the Octobot, a robot that bio-mimics the octopus to achieve realistically creepy underwater movement. Like the real eight-legged cephalopod, it has no skeleton, instead using its muscles to stiffen its legs as required.
The Octobot, from Livorno, Italy, has coils of shape-memory alloy inside its legs. These return to a previously "programmed" shape when a current is passed through them, causing them to heat up. By sending current to different coils, and combinations thereof, the arms can be moved in all kinds of ways, without a central motor system. The legs also have cables inside that stretch and contract, allowing them to push the robot along. This, too, is similar to how a real octopus walks.
Another trick was to mimic a biological trait called "embedded intelligence," where a limb seems to think for itself. In this case, the Octobot's arms are sensitive to the water movement around them, and are designed to react to the changing environment. This lets the 'bot issue a simple "swim" command to its legs, and they take care of it, working independently but in concert to move the whole robot. This requires way less computing power than trying to finagle each leg to perform the very complex action of swimming.
Possible uses? Exploration, and possibly rescue, but mostly this is just a great piece of robot design, and its principles could be applied to more practical robots.