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Apple changed their in-app purchase policy and ebook vendors were forced to close their integrated stores. Rather than just direct you to the web browser to buy ebooks, Amazon created a web-based ebook reading experience where you can buy ebooks and read them in online or offline modes right from within the browser.
Check out my full ZDNet Mobile Gadgeteer post for more details on this reading experience.
You are presented with a pop-up explaining how you are going to get books into offline mode by increasing download storage to 50MB, which should hold quite a few books.
As you step through the process you will see easy to understand directions and prompts for action.