The application is free, but the books, of course, need to be purchased from Amazon directly and transfered to the iPhone/iPod Touch; if you want to do it on the iPhone, you'll have to do it through Safari.
If you've purchased a book on the Kindle, you can freely transfer it to your iPhone and iPod Touch; you can also browse the Amazon's catalog on the iPhone, bookmark pages, and view annotations created on the Kindle -but you cannot make new ones. You also cannot transfer subscriptions for magazines and blogs from the Kindle to the iPhone, but you can already access those from the iPhone so it's not a big deal.
This is a smart move from Amazon. They could have stuck with the Kindle and shunned all other devices in order to retain more control and make more money on the hardware, but what they're really interested is selling ebooks, and spanning the Kindle delivery system accross multiple platforms is a better way to do it. I'd like to be able to buy books directly in the iPhone application, though; users that are really serious about reading will buy the Kindle because of the better and bigger screen, so there's no need to hamper the iPhone version in any way.