Where does a worm gear work?

It is used to change the direction of rotation. For instance on a rear wheel drive car the engine drive train is rotating in an axis running the length of the vehicle so all that spinning would be wasted if it the direction wasn't changed to cause the rear axle to turn in an axis running from side to side. The worm gear in this application is called the "pinion" and the wheel is called the "ring". so pinion is rotating clockwise and as it engages the ring gear it changes the lateral direction to cause the axle to turn.