DRM, or Digital Rights Management, is a way of locking an ebook 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 ebooks 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 ebooks 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 ebooks 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 ebooks are locked with DRM. Many publishers and authors choose to sell ebooks that are DRM-free. With DRM-free ebooks, 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 ebooks. You can find many of them here: