To be clear, the Kindle book you buy is good for all your devices. So I have a Kindle, 2 iPads, 2 iPhones, a few Macs, a few windows machines, and I can read any book I bought from the Amazon Kindle store on any of those devices. All the books show up as archive items and you can just download them at any time.
On top of that the "cloud" knows what you read last, and how far you read so if you open a book on one device, read a bit, then open it on another device - that second device will ask if you want to sync to the farthest read page.
All these benefits only work with Amazon bought books. If you put a mobi file or pdf - then you have to sync it to all devices via computer.