EPUB is the universal format accepted by virtually all publishers and read by virtually all e-readers. MOBI (and its descendants, like the KFX and AZW3) are best for publishing on Amazon's Kindle Direct Publishing marketplace.
Does Kindle use PDF or EPUB?
EPUB is a common ebook format around the web, but the Kindle can't read it natively. That's okay; you can convert . epub files to Mobi files for the Kindle to read. The key is a free piece of software called Calibre.