DRM, or Digital Rights Management, is a way of locking an e-book to work only on a particular device or to limit its use.
The main goal of using DRM is to protect against piracy. Unfortunately this rarely works, and instead raises a number of consumer rights issues.
DRM'd e-books locked to a particular device, such as a Kindle, can't be moved to a different make of device if you decide to switch. You can't read e-books you bought from Amazon on a Kobo or Nook, and you can't gift them to a friend.
Adobe runs another type of DRM, and most DRM'd books outside of Amazon use this. Without an Adobe ID - for which you hand over your personal details - you can only read most DRM'd e-books on the first device you download them to.
In effect, you never really own books locked with DRM - you only licence them.
Fortunately, not all e-books are locked with DRM. Many publishers and authors choose to sell e-books that are DRM-free. With DRM-free e-books, no matter what device you choose to use, you'll always be able to read the books you have bought, as long as you keep them somewhere safe.
There are a number of online bookshops that sell DRM-free e-books. You can find more information here:
Where can I buy e-books?