It seems to me that today's American culture tends to focus solely on the Allied invasion of Normandy when discussing June 6, 1944. My question is what else was happening on that day? What was going on at the eastern front? Italy? The continent of Africa? The Pacific Theatre? What were the Allied governments doing at that time?
In the East the Soviets were wrapping up the Winter/Spring campaigns. In the North they were winding down the Leningrad-Novgorod campaign, which had lifted the multi-year siege of Leningrad. And they were preparing for campaigns against Finland and the Baltics. In the South the Soviets were wrapping up the liberation of the Crimea and most of the Ukraine. There they are preparing for the Lvov–Sandomierz offensive where they will inflict a quarter million casualties on the Germans. But the big one which would start a couple weeks after Normandy was Operation Bagration where the Soviets would over the summer obliterate Army Group Center, in perhaps Germany's greatest defeat. All of these were timed for June so as to prevent the Germans from transferring forces to the West. And all were larger in scope than what was going on in Normandy. The smallest of the three, in the North, involved just under a million Soviets. The largest, Bagration, involved around 2 million men on the Soviet side.
In Italy the Allies had just broken through the German defensive line and were moving again. On June 4th they captured Rome. But before too much longer they would bog down again. As General Clark let the Germans slip away and set up a new defensive position while he took Rome.
In the air, bombing campaigns continue. But the focus is on interdicting German troops. So rail lines, bridges, and communications to Normandy are among the heaviest targets. But in the weeks prior, allied bombers were ranging all over Europe, as far to the South and East as Romania. On the 13th of June Germany launches the first V-1 bombing raid.
In the Pacific the New Guinea campaign was advancing. MacArthur had just landed on Biak on May 27th. On June 5th the Americans set sail for Saipan. They will begin landing on the 15th. And this will lead to "The Great Marianas Turkey Shoot" on the 19-20th, where the Japanese navy fliers are soundly beaten.
Along the Burma India border the Japanese are being driven back after a failed attempt to advance into India and take Imphal. This includes not only British troops, but a special American unit, "Merrill's Marauders" and several Chinese divisions.