Taxes, calculus, string theory, the way people vote—these are among the things that will never be clear to me. Advances and royalties, however, are pretty simple, so it's a shock every time I'm reminded how many authors and illustrators don't know how it works.
So an editor calls you up and says, "I'm very excited about this manuscript, and I'd like to offer you an $11,000 advance against a 5% royalty."
What do you say?
Now, for god's sake pay attention. You say, "That's wonderful! Could you tell me what print run and price point you've got planned?"
The editor replies, "We're planning on a 12,500 copy first printing, and the book would retail for $16.99."
You say, "Thanks so much. This is very exciting, but could I have a couple hours (or days, whatever will make you comfortable) to think about it?"
The editor says, "Sure. I'll look forward to your reply."
Now you break out your calculator and use this equation: print run (12,500) x retail price (16.95) x royalty (0.05) = $10,618.75.
This dollar amount is what a 5% royalty will earn you if all of that first printing sells. This is your starting advance. As you can see, the editor has rounded up to the nearest thousand.
So that's good. Now you start negotiating.
If all of this has come as news to you, get yourself a good book like Negotiating a Book Contract and read it.