If you learned history the conventional way, you saw D-Day pretty much in terms of surface meaning – the opening of a Western Front, the beginning of the West’s drive to Berlin…well, the Elbe, anyway.
But the importance may have gone well beyond the operational. Had it not worked, or not been attempted when it was, the Eastern Front that ate up 2/3 of the German war effort might have gone away, allowing Germany to focus on its western and southern flanks:
There is ample evidence that Soviet and German representatives had met in Stockholm for serious talks. Hitler saw Stalin’s opening as a sign of weakness. Understanding the tension between the Soviets and the Americans and British, he didn’t believe in 1943 that they could mount an invasion. Since Stalin himself had doubts, Hitler drove a hard bargain, demanding that Germany retain the land it had already won, particularly Ukraine. The talks broke down, though contacts seem to have continued.
Had the Allies not invaded Normandy in 1944, it is reasonable to assume that Stalin, whose troops were still fighting far inside their own country, would have accepted the deal with Hitler, since he likely could not continue fighting without a western front or at the very least could not regain the territory on his own. Churchill, it should be noted, was never enthusiastic about the invasion, either because he feared the resulting losses would be the end of the British army or because he wouldn’t have minded if the German-Soviet war continued so the Allies could intervene at the last minute, while nibbling at Greece. Either way, Roosevelt rejected Churchill’s view, sensing that the Soviets would make peace without an Allied invasion.
Without D-Day, Europe would likely still be controlled by the Nazis.