D-Day, which is sometimes thought to mean Departure-Day, is the name given to the invasion of Europe by Allied troops under the overall command of General Dwight David Eisenhower on June 6, 1944--the official name given to the operation is Operation Overlord. In a practical sense, D-Day began in the early morning hours of June 6, when about 24,000 American, British, and Polish paratroopers landed behind the main assault beaches to secure bridges, roads, and causeways to allow the main body of troops to land on the beaches and move inland quickly. Beginning about 6:00 a. m. on the morning of the June 6, approximately 160,000 British, American, and French troops began the assault on several beaches in the province of Normandy, and that assault is usually what is meant by D-Day. Supporting the invasion were almost 7,000 naval vessels from several countries (for the most part, America and Britain).
British and American troops landed on designated beaches on the Normandy coast, and casualties varied widely depending on the location. On Utah Beach, the westernmost beach, the American 4th Infantry Division landed about 27,000 men, with fewer than 200 casualties. On Omaha Beach, on the other hand, the American 1st and 29th Infantry Divisions landed about 50,000 men, with slightly more than 5,000 casualties, a much more significant casualty rate than that suffered by most other troops on other beaches. Overall Allied casualties attributed to D-Day were about 120,000, and about 6,500 for the Germans. The discrepancy is the natural consequence of the Allies being the attackers, and the Germans, the defenders.
Although the Allied timetable for securing the beaches and moving inland was not met, after the second day of landings, it became apparent that the Germans would be unlikely to succeed in pushing the Allied forces back into the sea, and by June 9 or 10th, the Allies believed that at least the initial invasion was going to establish a foothold in France.