It's a video tape format that does indeed mean "Digital Video". Sony invented it, and most camcorders labelled DV are the 'Mini DV' Format.
Picture and sound information on the tape is stored digitally (as 0's and 1's), rather than analogue as is the case with older formats like VHS,VHS(C),8mm and Hi-8.
As well as being better quality in the first place, the advantage to the user is that, that footage can be loaded on to your computer (as 0's and 1's) via a Firewire cable, edited, manipulated and then recorded back to tape or burnt to DVD without any loss of quality whatsoever. Unlike the old days of editing VHS to VHS, where quality on the edited copy was significantly pooorer tahn the original.
Hope this helps.