From the National WWII Museum:
Many explanations have been given for the meaning of D-Day, June 6, 1944, the day the Allies invaded Normandy from England during World War II. The Army has said that it is "simply an alliteration, as in H-Hour." Others say the first D in the word also stands for "day," the term a code designation. The French maintain the D means "disembarkation," still others say "debarkation," and the more poetic insist D-Day is short for "day of decision." When someone wrote to General Eisenhower in 1964 asking for an explanation, his executive assistant Brigadier General Robert Schultz answered: "General Eisenhower asked me to respond to your letter. Be advised that any amphibious operation has a ‘departed date’; therefore the shortened term ‘D-Day’ is used."