Can Someone Explain MMORPG's to me?

[AareDub]

The concept has always intrigued me, but I don't quite understand how they work. I used to think they were pretty much like a chat room except everybody had a character or something. Then I learned they actually have stories and things to go with them. That's where it gets confusing for me.

I know there is a superhero type mmorpg where you can go around the city with the other people and fight cpu controlled villians to level up, but are the cities really big enough where you don't have like 100's of people fighting the same 3 monsters? Are there individual servers like in fps online games where each one is entirely seperate, or do they (i.e. does the story) link up all together somehow? I can't even begin to comprehend how the story thing works with more than 1 person, is it like a free roaming thing then you decide to start the story together with some people? If you sign off can people finish the story without you? I can't imagine that they expect the same people to always be on at the same time right?

There's too much here I don't understand, if anybody is willing to try to explain ANY of it to me, I'd appreciate it.