How important was the Suez Canal to the Allies during WWII?

The Suez Canal was important mostly to the British, but it was very important to them. They needed to move large amounts of raw materials to Britain, where their industries were, and move the products to where the fighting was. This was strange to much of the US Army leadership of WWII, and they took some time to take it in.

The Americans were used to being based on a continent that had sources of almost everything, and had trouble adjusting to the way that the British got so much from overseas. This wasn't just for "ruling the empire", it was critical for all sorts of materials and manpower.

While the British Isles had quite a lot of manpower and lots of coal, they were deficient in many of the other materials needed to create military power. British power was crucially dependent on sea transport, and there was always a shortage of ships. If ships coming from India and Australia have to go around Africa, lots of them are occupied making that voyage, and the number of cargoes they can deliver per year goes down.

Britain imported food and raw materials and produced manufactured goods - in wartime, largely weapons and munitions. Those then had to be shipped to where they were needed, along with troops to use them.

For the Germans, taking the Suez Canal would badly damage the British ability to supply armies in the Middle East from the UK. That involved sailing around Africa and using the canal at the end of the voyage, but that was better than not being able to get stuff there at all.

The Germans would also gain a relatively easy route to Iran for oil, which the Germans were always short of. Getting it back to Germany would have been the next problem, but Rommel wasn't immediately worrying about that. Taking Egypt would also have deprived the British of bases, ports, hospitals, training centres and other infrastructure that contributed to military power.

For the British, holding Suez was only part of the problem. If Italy could be removed from the war, and the German forces in the Mediterranean Sea reduced sufficiently, it would no longer be necessary for supplies to sail round Africa. This would significantly increase the throughput of the available shipping, allowing the generation of more military power.

This was why they wanted the invasions of French North Africa and Italy: to increase the amount of military power they could wield. Without those things being accomplished, the Suez Canal was only useful for bringing troops and supplies to the Eastern Mediterranean around Africa - but without it they would have had to concede the entire Mediterranean.

I'm not clear as to just why it took time to get this idea across to the US generals. The US Navy understood the idea thoroughly: it's basic naval grand strategy.

Source: Masters and Commanders, by Andrew Roberts, an excellent book on Allied conferences and high-level decisions in general.

Advocating Overlord by Philip Padgett discusses a related subject, the debate within and between the US and the UK about invading Europe. Padgett makes the point that the UK felt that a cross-channel invasion was too risky - understandable given their last 30 years' experience fighting in France - and were focused on invading through the "soft underbelly". This required the Med be kept open. They also (correctly) felt that US forces needed experience before any invasion of Europe or North Africa was attempted.

Addition: Taking the Suez Canal would also have given Germany and Italy the potential for access to the eastern coast of Africa. If they'd achieved that, they could have joined forces with the Japanese Navy, which was well worth avoiding.