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.
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/
Thanks