D-Day, or Operation Overlord, was an invasion led by the Allies. Their mission was to invade Normandy, France on the beach because France was next to Nazi Germany, and would allow the Western Allies to launch a direct strike (after much dilly-dallying in the Low Countries of course). This assault began on June 6, 1944. This is one of the famous battles in World War 2 as well as the largest naval attack in history.
The Western Allies knew that although 80% of the Nazis were trying to stop the unstoppable Red Army in the East, the Germans were better trained and more advanced and would be able to beat back a head-on invasion they knew about. They first used radio misinformation to trick the Germans into thinking the Allies were attacking Norway and a main attack would be at Calais. The Allies dropped fake dummies and metal strips that confused radar, as well as entire fake army and tank divisions near Calais. This was successful and Hitler moved the main defenses to Calais as a result.
During the invasion, there wasn't only one beach, but five of them. There was Juno, Gold, Omaha, Utah, and Sword in Normandy. The USA was responsible for launching the attack on Utah and Omaha, the easiest and hardest to take respectively. The British stormed the Gold and Sword beaches, and the Canadians stormed Juno beach. Free France also played a large role in the invasion. When the Americans arrived at Omaha, they were mowed down by heavy machine guns in the bunkers and heavy artillery. Omaha beach had the heaviest casualties but in the end, the Allies sheer numbers and total air superiority made them victorious. The Germans launched several counter-offensives but the Western Allies held fast. After the battle of Normandy, the five beaches had been cleared and the Allies rushed to liberate France.