The breaking pliers is a special stained glass tool that has smooth jaws that meet at the tip of the pliers. This enables the tool to reach over the top and bottom of the glass with only the tip coming into contact with the glass exactly against the score line.
The pliers handles are held at a right angle to the score line. The edge of the glass needs to be close enough (within 20mm) to the score line in order to use this tool, as the tip of the jaw needs to be against the score line. It is used in lieu of your hands when the piece being broken off is too narrow to be comfortably grasped by hand. When bending the glass, the top jaw comes down flat against the surface of the glass (that's why we want the smooth jaw) and as more bending pressure is applied, lateral/pulling pressure is applied. This tool can also be used to groze the glass by carefully nibbling away the edge, but grozing pliers work better.