ePUB can be read on devices like smartphones, tablets, computers, or e-readers. It is a free and open standard published by the International Digital Publishing Forum (IDPF). So pretty much everything with a couple of major exceptions.
AZW/Mobi is the major exception. Amazon has its own “Amazon Word” format, or so they say. If you have a Kindle, this is the file for you. It’s a bit tricky loading this on to your Kindle, but here’s a quick tutorial, courtesy of Amazon, that should help you out.