Explanation for YGO players:
The stack is just a fancy name for the chaining. It works almost exactly the same as it is in YGO (I won't get to their screwed up priority stuff, tho).
Explanation for everyone else:
The stack is used whenever you play a spell. When you play a spell, it goes onto the stack, meaning that it is "on the go". At this point, opponents can respond to it and such (e.g. counter it). Once both players cannot do any more, the stack resolves and whatever spell played last resolves first. And this continues without stop until the entire stack is empty (no spells left).
Usually most games don't use the stack all too often (I mean by having more than one spell on the stack). They are usually used when instants are involved (e.g. counterspells or removal), and sometimes that's few and far in between.
So the stack's always been there, just that you didn't know you were using it the whole time. I mean, some people still like to call it "chaining" when more than one spell is on the stack, but whatever works for you! :P