The first picture (picture 1) on the left is where the motherboard is located inside my computer.
The one on the right (picture 2) is a top-down picture of the motherboard. Click to enlarge the images.

What does it do?

The primary purpose of the motherboard is to allow other components to communicate to each other via the motherboard. It houses all the components and turns it into one "unit".

In other terms :
From picture on you can see that there are alot of bits plugged into the motherboards. Once a component is plugged in, the motherboard will allow it to interact with other components using its electronic circuits.

It is the foundation on which the rest of the computer is built.

Next : Motherboard in depth - What all those slots mean