The application loads in its usual fashion to the iPhone. However, you have to go to the web and to the Amazon page to get your books. You can do this from the iPhone or you can do this from the computer. You must go to Kindlebooks though in order to get the Kindle version. This is a slight flaw in the iPhone program, since really you should be able to buy the books directly from the program itself.
I did go through the purchasing part on my computer and was surprised to find that my purchase showed up on my iPhone almost immediately. The pages are well preserved and you can choose your font. I found it to be a little more responsive than Stanza, the de facto comparison, but a little less than Classics - the snazzy graphics intensive program that has limited open source books available.
What is nice about this is the fact that Amazon has an amazing library of books, both popular and obscure. I believe the quoted count for the Kindle was 204,000 (*1). To be able to access these without having to hook up to iTunes and sync over the air is just wonderful.
The software is 2.9 mb and is a version 1.0 product.
*1 (From Amazon.com as of 3/4/2009).
I should note that one can get similar functionality from Stanza, which offers a large selection of books. However, I do not believe that they offer either the pricing advantage or the sheer volume of books that Amazon does. However, Stanza is a great product that is a must have if you have an iPhone. The major differences appear to be in Stanza being a little more graphics intensive, which tends to run down the batteries a little faster. But both are very good.