It's not that Normandy was by itself a critical area. Rather that Normandy offered the best combination of a number of factors.

1. Beaches to land on. Somewhat obviously, the Allies needed a area with plenty of gently slopping beaches, with good access off the beach, to land their armies on. You can't very well haul hundreds of Sherman tank and 6x6 trucks up a cliff face. This rules out large areas of the European coastline simply because they're mostly, or all, cliffs.

2. Air Cover. The area needed to be within reasonable air cover range from bases in Britain. This makes the area on the west coast of France unattractive simply because of the distance that the planes would have to fly to get there. More flying time means less time over the beaches. Plus of course if you land all the way over there then that's further you have to go to get to Germany.

3. German Defenses & Likely Reaction. Actually the Normandy defenses were not as heavily defended as many other areas such as the area around Calais. This weakness was actually known to the Germans and they were already taking steps to correct it. More subtly, an invasion directly across the channel at Calais would immediately have triggered a very violent counter-attack since it would have represented a major threat to Germany. The Allies exploited this fixation with a deception plan that persuaded the Germans that a large force was just waiting to pounce on the Calais area if they moved significant forces to Normandy.

In summary, the Normandy invasion was primarily a way for the Allies to outflank the defense and forces in the Calais area. But keep the invasion area under air cover and not too far from Germany proper.

Good reads:

Rick Atkinson, The Guns At Last Light

Joe Balkoski, Omaha Beach

As /u/NoAstronomer says, Normandy was the easier way. Chapter IV of [Volume V] (http://www.ibiblio.org/hyperwar/NHC/books/comnaveu/index.htm) of the United States Naval Administration in World War II outlines the requirements for selecting the lodgement area for amphibious invasion including air, naval, strategic and logistic considerations.

The requirement for air cover from the UK ruled out areas west of Flushing or north of Cherbourg (the RAF's primary fighter, the Spitfire, had a relatively short range). Within that area, the Pas-de-Calais and Cotentin-Caen sectors had the most suitable beach capacities, but the Pas-de-Calais was problematic in terms of expanding the lodgement and, more immediately, securing the area during the initial assault. If you'll forgive a quick copy & paste from a [recent answer] (https://www.reddit.com/r/AskHistorians/comments/4m56ss/why_were_the_allies_of_ww2_afraid_of_the_defences/d3szknw):

The Pas-de-Calais was, very roughly, at least twice as well defended as the Lower Normandy beaches. German defences in northern France were under Army Group B, broadly grouped into the Fifteenth Army (AOK 15) sector of the Pas-de-Calais and Upper Normandy (from Dunkirk to Le Havre, around 700km of coastline) and the Seventh Army (AOK 7) sector including Lower Normandy and Brittany (covering about 1500km of coastline). Steven J. Zaloga's The Atlantic Wall (1): France has a breakdown of artillery, bunkers and obstacles by sector:

Artillery

AOK 15 had more guns than AOK 7 (670 vs 589) covering about half as much coastline, of heavier calibre (about 60% of AOK 7 guns were light (75-105mm) compared to 40% of AOK 15). There were several super heavy batteries in the Pas-de-Calais such as Lindemann, Grosser Kurfurst and Todt with guns of between 280mm and 406mm in heavy concrete casemates that could have fired on ships in the channel.

Bunkers

There were roughly similar numbers of bunkers in the two sectors (2,364 for AOK 15 vs 2,176 for AOK 7; Zaloga gives a further breakdown by type), again meaning more than twice the density of bunkers in AOK 15's sector due to the shorter coastline.

Obstacles

Zaloga breaks down types of obstacle (stakes, concrete obstacles, 'hedgehogs', mines etc.) by Corps, with an overall obstacle density per km figure; for 67 Corps around Calais it was 705, for 84 Corps in Normandy is was 223, again less than half the density. In particular there were more than twice as many mines laid in the 67 Corps area.

Troops

The [Official History of the Canadian Army in the Second World War] (https://www.ibiblio.org/hyperwar/UN/Canada/CA/Victory/index.html) gives the Fifteenth Army 18 "non-mobile" divisions along the coast and the Seventh Army 11, again a substantially higher concentration in the Fifteenth Army sector (there's also a [map of their deployment] (https://www.ibiblio.org/hyperwar/UN/Canada/CA/Victory/sk/Victory-3.jpg)). The situation of the panzer divisions in France was complicated by a disagreement between Rommel, who wanted them close to the beaches, and Rundstedt, who wanted to hold them back as a mobile reserve; as a compromise Rommel was given control of three, of which one was placed within striking distance of Normandy while the other two were north of the Seine.