Kindle supports various formats. Amazon's own azw, plus PDF, txt, mobi & prc (without DRM, i.e you can't buy a commercial product in mobi or prc format that has rights management, but you can buy one that doesn't); also MP3 and Audible audio. There are a couple of other formats supported by farting around with conversion software.
Some other formats can be converted for a fee by sending them to Amazon.
Finally, there are plenty of third parties that supply cheap or free books in either Amazon's own azw format or in a format that Amazon supports. These include Project Gutenberg (and freekindlebooks.org), archive.org and openlibrary. You may have the choice of dragging and dropping to the Kindle via a computer and USB connection (free), or have them emailed directly to the Kindle (not free).
The azw format is actually a very slightly modified version of mobi.
There's a huge amount of info on the Amazon site, suprisingly enough
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