Gödel's Incompleteness Theorem

Now what's all this shit about?
In plain, laymen english please!
(Calculus is the fartherst I'll ever bother with math)

I'm fascinated with everything it (seems) to imply but I'm not sure i quite get it.

Some religious people have used the theorem this way : "Since the non-existence of god cannot be demonstrated, he may exist". Opponents of religions coutered this argument : "Since the non-existence of the Flying Spaghetti Monster cannot be demonstrated, he may exist". I think that a sane way of thinking within the limits imposed by Gödel's discoveries is deductive thinking coupled with occam's razor.