special relativity - What is the Light Cone and we do we need it?

It is defined as $x\cdot x = 0$. How is this justified?

Also, why does the backward light cone need to exist? It is said that light emitted in a backward cone would pass through the origin. But why? Wouldn't it just create another forward cone with a different origin?

And the most important thing is: what is this Light Cone concept actually about? I don't see how this concept came about.