Points . . .

What are they, and how did I accumulate them?

They'll serve a purpose for name changing later on. You get them by posting.

So do people vote on your posts?

They're added when you post automatically.

So, does the amount of points earned depend on where you post? I notice that sometimes I get one, and others, I get two...

Posting topics gives you more points. posting in certain areas can give you more points while others can give you none at all (people usually do this with the spam section)

...
And how do you know all this, when you aren't even a moderator?

Experience, I would assume; or maybe he had his own forums on ForumMotion.
Your responses raise the question: What about the post whores?
EDIT: That's the first time I've ever used that word on the internet.

Well I've been an admin to about 5 or 6 forumotion boards, i almost know the admin control panel like the back of my hand D:

And post whores aren't hard to spot when there's only about 10 active members. We don't have to worry about those for a while

Understood.

...Oh, yes, can you lose points for things like double posting?

I can take away points if I see fit..

Sweet.