First, those big tentacles at the front are labeled as "SMA Arms," which means that they're actuated by a shape-memory alloy that changes is length when heated, no servos or anything necessary. The other six arms are silicone with a steel cable inside, and this steel cable is attached to a bunch of nylon cables, and by manipulating those nylon cables, the tentacle can be made to wiggle around and even grip things.
Read more and see a couple of videos of this mechanical calamari at IEEE Spectrum's robotics blog. Link -via Not Exactly Rocket Science