DRM stands for Digital Rights Management. It can come in the form of a simple CD check, or a fully fledged limited online activation, that has to be revalidated online every few days, for you to use the software. Basically, a restriction on how you can use the software. What GoG means by no DRM, is that there is no restrictions or limitations as to how you can use the games. They can be installed anywhere, without having to worry about having a disc in the tray, having an Internet connection, or anything of the like.
EDIT:
@Flashdrive
Indeed. But current gen DRM is more to stop casual piracy and second hand sales. Basically, it's just there because the publishers are greedy money grubbing bastards.
Post edited January 28, 2010 by sheepdragon