The box on the back of a motorbike is commonly referred to as a "top box" or a "rear box." It is a storage compartment attached to the rear of the motorcycle, typically made of hard plastic or metal. The purpose of the box is to provide additional storage space for the rider, allowing them to carry items such as helmets, jackets, groceries, or other personal belongings while riding. Top boxes come in various sizes and designs and can be removable or permanently fixed to the motorcycle's rear.