The Battle of Normandy was the first major campaign in the successful Allied invasion and liberation of Western Europe in World War II. It started on D-Day with the largest amphibious assault in history and ended with the retreat of German forces over the River Seine. Although ultimately a success, the campaign was marked by mis-steps, petty rivalries between generals, and dashed expectations of quick success - much more so than a cursory viewing of Saving Private Ryan or review of a school textbook might lead you to believe.
Placing the invasion of Europe into the larger context of World War II is important to understand what ultimately made it possible, and on the other hand why it took so damn long to bring it about. In 1940, German forces had blitzkrieged their way through France and forced the evacuation of British forces from Dunkirk. Then in 1941, Adolf Hitler invaded Russia (note to aspiring European hegemon: don't invade Russia) and began an initially spectacular advance. Uncle Joe started pressing the other Allies to open up a second front in Western Europe to relieve the pressure on his own forces, but the Allies kept Stalin for time.
Trust being as fragile as you might expect between a Communist dictatorship and the self-proclaimed champions of liberal democracy, the Allies in World War II were constantly concerned that the others might make a separate peace with Germany to save their own skins. Stalin was soaking up an enormous quantity of German manpower and equipment on the Eastern Front, which ultimately made the invasion of Normandy possible - but his constant pleas for assistance also partly led to the Allies first invading North Africa, then Sicily, and then Italy, in an attempt to take some pressure off the Reds and make sure they stayed in the game.
But plenty of other pieces had to fall into place before the invasion of Normandy was possible. The Battle of the Atlantic - the ongoing struggle to drive German U-boats out of the Atlantic and ensure the safety of the vital sea route between the U.S. and the UK - had to make major gains. A strategic air offensive designed to pin the Luftwaffe in a defensive role had churned through their capabilities with such effectiveness that the Luftwaffe only managed to fly 36 sorties against the Normandy beach heads on D-Day. Whole artificial ports that could be towed across the English Channel were constructed so that heavily-defended German ports would not have to be captured. The American and British armies had to be trained and developed almost from scratch.
When conditions were finally right in June 1944, Operation Neptune - the initial Normandy landings - was launched. The plan was to secure the beach heads quickly and then immediately start pushing towards major objectives to the south. Rather than getting trapped in a static war of attrition, which is what actually happened, the Allies had hoped to initiate what is called a war of movement - the use of fast-moving mobile capabilities to quickly break through the German lines and push south. Instead, the British completely failed to achieve their objective of capturing Caen on the first day - this was not achieved until late July. The Americans likewise failed to capture the port of Cherbourg quickly, and by the time they did take it the port facilities had been completely destroyed by the Germans and would take months to get back online.
A war of attrition of the sort the Allies had wanted to avoid is exactly what ensued. The Germans were unable to drive the invaders into the sea, but the Allies were likewise unable to break through heavy German lines. The Normandy terrain - a mixture of woodland and hedgerows known as bocage - made going on the offensive extremely difficult for both sides and highlighted deficiencies in training. Much of the British force had trained in the comparatively open country of Yorkshire and was not ready for this terrain; one unit which had happened to train in similar terrain in Kent fared much better. The Allies simply had little idea of the sort of terrain they were going to face before they got there; the War Office in London had even appealed for British patriots who had holidayed in Normandy in rosier times to send in their holiday photographs as a means of gathering intelligence.
Hitler, who narrowly survived an assassination attempt while the invasion of Normandy was ongoing, made matters worse for his own side by insisting on micromanaging decisions. This sometimes led to a delay of up to 24 hours while German forces waited for instructions to arrive from his retreat in Bavaria. Gunther von Kluge, the German commander in the West, was knee-deep in the group of generals who opposed Hitler and wanted him to sue for peace; after refusing the latest in a series of suicidal counter-attack orders from Hitler, he was relieved of command and then either committed suicide or was shot by the SS for involvement in the attempted assassination of Hitler.
The going was tough, but the Allies eventually managed to wear German resistance down. One of the main advantages was control of the air, which prevented the Germans from ever being able to amass a concentration of forces to counterattack without being spotted. However, controversy emerged and rages to this day over why it took so long for the Allies to break out of their beach heads and finally push south. Many Americans have blamed Field Marshal Bernard Montgomery for being overly-cautious and defensive, while the Brits tend to charge the amateurish Americans simply didn't understand that a plan rarely survived first contact with the enemy and that their man had simply demonstrated laudable flexibility. In fact, the morale of the British forces was generally low and Montgomery was much more casualty-averse than the American commander, Omar Bradley, simply because his country did not have the same reserves of manpower to draw on.
The steady attrition gradually wore the Germans down, while meanwhile the Allies amassed more and more forces on their beach heads. The break-out finally came in late July when the Americans launched Operation Cobra and drove decisively south; Monty meanwhile kept the Germans busy with less-ambitious operations which finally captured Caen, preventing the Germans from massing forces to oppose Cobra but also destroying Caen in the process. The campaign reached its crescendo in the Falaise pocket, where a large concentration of German forces were boxed in and then destroyed or captured. Monty, though, was heavily criticized for apparent timidity in allowing a large number of the German forces to escape and fight another day.
By late August, Paris had fallen and the Normandy campaign was over. Soon the Allies would drive into southern France and east towards the Reich. Quite why Monty might have wanted to so cautiously preserve his forces became apparent when he insisted on Operation Market Garden an ambitious airborne assault in Holland which aimed to capture bridges over the Rhine and get the Allies into the Reich by Christmas - an operation in which he ensured he would largely be credited with the success. When the operation went wrong, he ended up credited with its failure instead. The unseemly race between the Soviets, Americans and British to be first into Germany - often at the expense of the lives of their men - had a deeper significance, however. For the Normandy campaign had marked not only the beginning of the end of the Reich, but also the beginning of the divvying up of Europe between the West and the Soviet Union - a pattern of territorial conquest in which what was occupied during these heady days would largely stay on the same side of the Iron Curtain until the end of the Cold War.