Amazon-Kindle Format is also known as Mobi format and is based on the erstwhile OeBPS (Open eBooks Publication Structure). The .mobi files can be read on a Kindle Reader System (Amazon-Kindle hardware + software) or simply a Kindle software on your own reading device, may it be a Windows PC, Mac, Blackberry, iPhone, iPad, or an Android. The Kindle software can be downloaded from here.
.Mobi files can also be read on a Mobipocket Reader.