D does actually stand for DAY. You will also find the term H Hour used, and again H+1 etc. When the military make plans for the future they are usually not aware of the actual start day and plan in terms of dates relative to the start.
So D day and H hour is taken as the start and other operations planned relative to that date. Such that if D day and H hour are (say) 0430 hrs 6th June, then boats must start loading at H-18 (say), paratroops land at H-12. Shore bombardment at H-1, with the landing at H hour.