Kindle's file format is MOBI and it is a quick and simple process to convert from ePUB (whilst also keeping the original file for reading on multiple other devices). Watch the how-to video below to see how simple the process is.
You need to download and install the free, open source, Calibre app to convert your ePUB files. Calibre also does lots of incredibly useful things, such as organising your eBook library and syncing specific books (or other text files) with your various devices, but most users simply use it to convert files for reading on Kindle!