A motherboard is the heart and power of any general computer and plays an equally important role. It is the main printed circuit in any computer and through a series of cables and parts, all devices such as the memory, hard drives, video and sound cards are connected to it as one single platform.
The backplane is a printed circuit board that contains connection slots for expansion boards and allows for communication between all connected boards.
There are 2 types of backplanes, an active backplane which contains the slots and all needed to manage communication between these slots and a passive backplane which only has the bus connectors. In a passive backplane all data communication is between them is handles by expansion boards connected to the backplane.
There are different size motherboards and backplane dependant upon your application.