Ninefingers posted this incredible useful text over at meta.crypto.stackexchange.com. I’ll just copy it.
Rationale: why do we close questions?
There are really two ways to do moderation. If you've been on any of the
SE is slightly different - it works the other way. Anyone can ask a question on SE and closing a question is the equivalent of putting that question back into review/improve mode. It's a feedback mechanism designed to react to problem cases only, so the usual business of asking and answering good questions can just... happen.
Why do we close a question?
The philosophy of SE is that each site handles questions on problems you face or things you are trying to understand. The don't ask section of the FAQ gives you a good overview of things that don't work - to summarise:
These have been worked out over time and with a lot of experience from Stack Overflow and are, broadly speaking true. Sometimes, exceptions are made - it is always a case-by-case thing.
Is closing like deletion?
No. Actually, deletion is a different concept on SE. Closed questions are put "into improve mode" if you like, and are still visible for anyone to improve. That's the idea. Deleted questions are different - they have a red background and are invisible to all but high reputation users. So deletion is different and solves a slightly different problem.
What are the requirements for closing a question?
If you have 500 reputation on the site currently, or 3000 reputation on a graduated site, you can vote to close any question for the reasons above. More on that in a moment.
If you do not have this level of reputation, you will find that under the flag menu, you have an option "this question does not belong here". That will raise a flag for users who can vote to close.
Why can anyone vote to close/reopen?
Firstly, anyone can vote to close or reopen (or flag as such) because it is your site. This is really important - it's about expressing what you feel works and doesn't.
How are moderators different?
Moderator close votes complete the required vote count immediately, no matter how many people have voted. This applies for both close/reopen votes.
Initially, as the reputation requirement rules out many users, you will see moderators doing most of the closing to guide the site and look after the content. As you gain in reputation, you get to join in.
Ok, so how does it work?
Ok, the important piece. Voting to close works like this:
How does vote to re-open work?
A closed question has a "reopen" link underneath it. If you click this, a dialog box will ask you if you are sure - click yes and your vote will be registered to re-open the question.
Below, you can see an example of the re-open link with two votes registered for re-opening (out of five).
What happens if I make a mistake?
Don't worry! Unless five people agree, or a moderator agrees, the question won't be closed.
I've seen a closed question and I disagree. What can I do?
Well, one option is to use your re-open vote! You can also always raise a discussion here on meta to seek clarification on why a question is closed and hopefully either a resolution will be reached, or you will get an explanation for the closure.
My name appears on the bottom - isn't this going to cause problems with other users?
Actually, surprisingly few closed questions generate any response at all.
However, if you experience difficulties as a result of closing a question, you can and should contact a moderator via the flag mechanism (which is anonymous). We can then take any necessary action.
How do I find questions I might need to close? What about re-opens?
Actually there are two tools for this.
My own summary after a long reading session
Closing is not deleting. A closed question is still visible, it can be improved and reopened. It doesn’t affect the accept rate but prevents potentially useless answers. Help us to stay on focus, use your close votes.