This apparatus allows holding an unfinished guitar body in a vise without damaging the delicate wood body. The builder uses this devise to position the guitar body to allow them to add wood structure elements to what is the interior of the guitar body. At this point of the construction the builder is cutting and shaping small wood pieces to add strength to the body. After cutting and shaping these parts they will then use a guitar glue that is specially formulated to not dampen the sound made by the instrument.
The round wood pegs that you can see going around the outside of the guitar body, have a threaded metal stud in the bottom, which is held in place by a wingnut, this allows the builder to remove these pegs selectively when they need to glue in something to the body of the guitar. By being able to just remove a peg or two, they still have most of the other pegs in place to hold the guitar body.