Motherboard is the one of the main components of a CPU as it holds and connects all the other components of a CPU ,i.e., RAM, processor, graphics card, hard-disk, etc.
There are several ports on this board which are specifically designed to connect the components. Motherboards come in different form factors (it means different sizes and capacities) according to which a buyer can buy these according to their needs. It allocates power and allow all the other hardware to communicate.
A motherboard is placed in a CPU cabinet using standouts, which holds motherboard and once it is placed, all the other components can be connected.
This is an image of a motherboard manufactured by the company Asus along with different parts of a motherboard labelled.
Since there is a term motherboard, there is no such term as fatherboard, infact there is no need for one such term.
The first motherboard is considered to be one used in the IBM Personal Computer, released in 1981. At the time, IBM referred to it as a "planar" instead of a motherboard. The IBM Personal Computer and the motherboard inside it would set the standard for IBM-compatible computer hardware going forward.