To start, it has quite a few different names. Motherboard, as in the "mother" of all components attached to it, system board, planar board, mainboard (more commonly used to describe boards without expansion slots), and logic board. Simply put, it is the foundation of every computer. I prefer the term system board because it is the board that connects all the components together and makes the computer a system of interrelated parts.
I'm pretty sure a lot of different devices, even outside the realm of desktops, laptops, and servers, use system boards. I would think a router and a switch would use a system board although I am not sure. I will do more research on those devices when I get into Network+ or CCNA.