For this example, I'll keep it real simple (for my own sake and well as yours). Let's say you acquire an agent and sell a novel. The publishing house offers you royalties of $3 per book sold. 
      It's probable that you'll be given money in advance - more specifically: an advance against royalties. What this means is that they give you a lump sum of money before the book comes out as payment that's yours to keep - say, $60,000. However, the money is not in addition to royalties, but rather part of royalties - meaning they've given you royalties for the first 20,000 books (times $3/book) upfront. Since they've already paid you the royalties of the first 20,000 books, you will not starting actually making $3/book until you sell the copy 20,001.

Think of it like this. When you get hired at a new job, you ask for several months pay upfront and the boss agrees. It's not a separate signing bonus you're getting - it's your hard-earned money paid to you early. You get the lump sum quickly, but then you don't get paid again till the regular checks start months later.

Many things to consider:

• Royalties per book vary greatly. If you get $3/book, that's pretty darn good. If you write a typical nonfiction book, you may just get $1/book.
• Advances against royalties are a pretty sweet deal. You get a lump sum upfront, which you get to keep even if the book fairs poorly.  (Repeat: The advance is yours. Period.) But if the book takes off, you will start getting royalties down the road.
• Reality check: Be aware that the money amount promised will hit your bank account as a lot less than expected, as Uncle Sam will take a big cut and your agent takes 15%.
• You may run into a "flat fee" situation, where a publishing company pays you one sum of money upfront with no talk of royalties. This is legitimate - just make sure it's what you want.
• It's common for a house to break up the advance. They may give you $30,000 when you sign the contract and then $30,000 upon completion of an acceptable manuscript. On this note, make sure you turn in an "acceptable manuscript," so that you get to not only receive the second payment, but also keep the first one, and not have a publisher demand it back.
• Read your contract thoroughly. It's all spelled out.

Want more on this subject?

• Will agents try to scam you with small costs? Find out here. 
• On this subject, know that advances are getting smaller.  
• Confused about formatting? Check out Formatting & Submitting Your Manuscript.
• Read about What Agents Hate: Chapter 1 Pet Peeves.
• Want the most complete database of agents and what genres they're looking for? Buy the 2011 Guide to Literary Agents today!