As a matter of interest, the French refer to it as ‘J-Jour' on precisely the same basis as we say 'D-Day'...ie ‘jour' is their word for ‘day'.
The earliest written record of the phrase comes from a World War I Field Order of 7th September 1918. That's a whole generation before THE D-Day of 6th June 1944 in Normandy. The Order reads:-"The First Army will attack at H-hour on D-Day with the object of forcing the evacuation of the St Mihiel salient."
The reason for the code was so that planners could say 'D-Day minus one' to mean the day before the off or 'D-Day plus two' to mean 'Two days after the start' etc. Also, of course, it concealed the actual date from the enemy. All-in-all, D-Day both is and means 'Day with a capital D'. It's what we might call today 'The big one!'