That style of clamp is called a cantilever clamp. They're extremely handy for when you want to clamp stuff without the clamp faces twisting due to the screw, hence the popular brand name Kant-Twist.
The pads are copper plated steel to help keep any spatter or metal transfer to a minimum.
I use them all the time in the machine shop and welding department. Very useful. The grooves in the pads allow you to easily grip round stuff and the design is inherently low-profile so you can use them in a milling machine or something without the screw sticking up.