Digital Rights Management, or DRM, is an important concept to understand for users of electronic content.
"Think of DRM on an eBook as a lock, with your eReader having the key to open the lock and display the file." -- Jason Griffey
There are different DRM systems, and it is important to know what type you are using. With Overdrive ebooks, the DRM for ePub file formats is handled by Adobe Digital Editions; but for Kindle ebooks, Amazon uses its own DRM system.
DRM is related to file type: the Kindle does not support the ePub format that is the standard format for ebooks, which is why you can't download Kindle ebooks onto your ePub-supporting ereader, or why your Kindle can't read ePub ebooks.
So, choosing an ereader can limit you to a particular online bookstore because of DRM. When choosing a device, make sure you know what online bookstores you can and can't access with your device.
The best explanation of file type and D.R.M. is this article.
A list of common filetypes related to audiobooks and ebooks is available back on the Downloadables Support page.