It is a double headed c-clamp. The two heads help you achieve the same total clamping force as a regular c-clamp, but it spreads the force out over twice the surface area so you are less likely to dent or damage a softer wood for instance when gluing and clamping.
The clamp you have is nicer than most of the ones made today, because the newer ones usually only still have a single round end on the threaded screw (instead of the double head yours has) which can end up defeating the purpose. I attached a picture of the newer style that is the most common so you can see what I mean.