A vibrating motor is essentially a motor that is improperly balanced. In other words, there is an off-centered weight attached to the motor's rotational shaft that causes the motor to wobble. The amount of wobble can be changed by the amount of weight that you attach, the weight's distance from the shaft, and the speed at which the motor spins.
This type of motor can be used affixed to all kinds of objects, which will cause them to vibrate and move freely about. Vibrating motors can be found inside cell phones, pagers, gaming controllers, and personal massagers.