The Amazon Kindle can use .mobi file formats directly. It doesn't support the other common ebook fileformats like .epub
Luckily it's easy to convert from one format to the other. Caibre contains a handy command line programme called ebook-convert that will convert ebooks from one format to another.
Sample usage
ebook-convert book.epub book.mobi
It will automatically detect that you want to convert it from epub to mobi. As it's running it'll print out some stuff to the command line, that can be ignored. It can take a few minutes to convert, the longer the book the longer it'll take.