The authors say that this is the first draft of the book submitted to the publisher, so I suppose it's nearly complete?
More details available at the site they put up, http://banditalgs.com/
Say you are selling a product and you are AB testing something related to buying the product. When a user visits the site you ideally want to give him the version you are more confident is better. By using a bandit approach you can determine if say option A is currently better (w.r.t. some confidence bounds). After each visit you can update the bounds and after sufficiently many visits you have a winner. The main difference to more traditional AB testing is that the process is more adaptive and less time is wasted on exposing an inferior product to the user.