Hi Lori, and welcome to mobileread !
DRM means "digital rights management" or "digital restriction management" depending on who you ask.
it is basically a sort of "lock" on digital media (mp3s, ebooks, etc.) which will limit the ways in which you can access the media. for instance, drm can be used to "lock" an ebook to a specific device, which means if you get a new device, you won't be able to read the books you already have. for a more complete article, please take a look at our wiki :
DRM. although editors claim that drm is used to prevent illicit copying of files, most people dislike drm because it ends up restricting "fair use" more than anything else, locking customers out of access to media they have legitimately purchased (a kindle owner cannot read their kindle books on a sony device, for example, unless they remove the drm). i hope that makes it a little more clear to you ; don't hesitate to ask if you still have questions. and take a look around the forums as well for many other discussions about drm and other aspects of ebooks. happy reading !