formats for e-books, in the same way doc, docx, wp, rtf are formats of word processor documents and gif, jpg, tiff etc are image formats.
Rights management roughly means a purchased file can only be viewed on the device it was bought for: if you give the file to someone else, they won't be able to read it on their device. Free stuff almost never has rights management present, paid stuff usually does. A good comparison would be with music you create or download in mp3 format and music you buy through itunes.
You've got around 700,000 paid products directly available for Kindle, and around 2 million free ones directly or indirectly available. Plus you can convert many of your own files to Kindle format either on your PC or by piping them through Amazon for a fee.