The application is free. When you run it the first thing you do is to register it to Amazon’s web site (using your normal Amazon username and password – you already have one, right?) As far as the Amazon site goes, your iPhone is a Kindle. It shows up on your list of Kindles. And you can buy books for it. So now you can visit the Kindle Store on Amazon and buy books (and free book samples)
Now on my iPhone, magically, those books appear on my book list, and I can read them. There’s a huge collection of books and particularly nice, free initial chapters for a ton of books.
Here’s the genius part: I get a free app, experience the Amazon Kindle Store, get a bunch of free books and read them on my iPhone. The iPhone is a crappy ebook reader. The screen is too small: Solution: I guess I need a Kindle. Genius.