This camera set-up utilizes an attached gimbal that can rotate freely along 3 axes, so that the camera may stay in place during jerky movements. With this device, a cameraman can avoid shaky camera motions (such as the Cloverfield technique) and instead allows the camera to be stable and unaffected by factors such as terrain and wind. Here is a video showing off two similar shots, with one of them using a gimbal mounted camera:
In movies, this technique can also be used to give off a feeling of flying or floating. For example, in the final maze sequence in The Shining, the camera follows both Danny and Jack with swooping and smooth motions, thanks to the gimbal:
There are several companies that specialize in in mounted gimbal cameras, such as Cloudcap Technology, and more common brands such a Canon and Nikon.