The term D-Day is used generically by the military to simply mean the day on which a combat attack or operation is to be initiated, but it is often used to refer to the Battle of Normandy of June 6, 1944, which marked the commencement of the liberation of mainland Europe from German occupation during World War II.
The terms D-day and H-hour are used for the day and hour on which a combat attack or operation is to be initiated. They designate the day and hour of the operation when the day and hour have not yet been determined, or where secrecy is essential. The letters are derived from the words for which they stand, "D" for the day of the invasion and "H" for the hour operations actually begin. There is but one D-day and one H-hour for all units participating in a given operation. It is unnecessary to state that H-hour is on D-day.
When used in combination with figures and plus or minus signs, these terms indicate the length of time preceding or following a specific action. Thus, H-3 means 3 hours before H-hour, and D+3 means 3 days after D-day. H+75 minutes means H-hour plus 1 hour and 15 minutes.
Planning papers for large-scale operations are made up in detail long before specific dates are set. Thus, orders are issued for the various steps to be carried out on the D-day or H-hour minus or plus a certain number or days, hours, or minutes. At the appropriate time, a subsequent order is issued that states the actual day and times.
The earliest use of these terms by the U.S. Army that the Center of Military History has been able to find was during World War I. In Field Order Number 9, First Army, American Expeditionary Forces, dated September 7, 1918: "The First Army will attack at H hour on D day with the object of forcing the evacuation of the St. Mihiel Salient."
D-day for the invasion of Normandy was set for June 6, 1944, and that date has been popularly referred to by the short title "D-day." (In French, it is called jour-J.)
Source: The General Service Schools, Fort Leavenworth, Kansas, Combat Orders (Fort Leavenworth, Kansas: The General Service Schools Press, 1922).