Check the faq on TexasWrens site http://www.texaswren.com/
A bookring is a group where the book travels from one person to the next on the list, ending up back at the person who sent it. Check the FastFood nation ring listed. It will start with Seferim, who opened the Bookring, go through each person on the list, who reads and journals it, then back to Seferim at the end.
A bookRAY is the same thing, but the last person on the list releases it into the wild instead of sending it back to the person who opened the Ray.
BookBox, same thing, but it's several books in a box that travels to each person on the list. Say you started a Science Fiction BookBox. 10 people sigh up. You start with any number of scifi books, say 5. You send it to me. 3 look good to me so I take those out and put in 3 more. Send it to the next person who takes out as many as they want, replacing with like number. On it goes until it comes back to you.
Ring, Rays and Boxes can be international, or strictly within certian Geographical boundries. Say, only in US/Canada. or an all-Italian bookring. If you choose to open an international bookring, ask people to let you know if they can send international. The cost could be several dollars difference, and some people are on budgets. $1.95 to Canada vs. $10 to the UK for instance.
Hope all that helps.