If you seize the Suez Canal you make any shipments from India, or Australia have to go all the way around Africa, instead of cutting thousands of miles off and going through the Med. You deny the Royal Navy one of its primary conduits for shuttling ships back and forth and add significant time to convoys bringing reinforcements from the Commonwealth.

And the best way to get to the oil fields of the Middle East, when your navy isnt all that great, is by land, the shortest route is through Egypt.

/u/DBHT14 gave clear picture of strategic implications for North Africa; and to make it clear: The British already had a Middle Eastern Command at the start of hostilities in N. Africa. It was small, the command was strategically important but operationally a backwater, and the Germans had no intention initially of doing anything other than riling up Muslim leaders and Egyptian Army Officers via espionage.

Italy however, had clear-cut colonial desires in North Africa that would bring them straight into conflict with the British. Jack Greene and Alessandro Massignani have termed this the "Parallel War" - Mussolini essentially attempting to capitalize off the war situation with attacks that inherently benefited Italy, but had no larger impact on Axis war goals.

The problem is it backfired; and the Italian 10th Army was vigorously counterattacked and smashed by only two British Divisions, the Indian 4th Infantry and the British 7th Armoured, with supporting elements. The disaster was so wholesale that Hitler immediately dispatched elements of several light and Panzer divisions in a corps-sized element to block and cover the Italian retreat. The Afrika Korps was born.

From there the narrative gets foggy, and depending on whom you read, the fault either lies directly with Rommel or with OKW (German High Command)... despite the build-up for Operation Barbarossa (the invasion of Russia) occurring at the same time, the Afrika Korps is slowly built up into a (very small) Army-size formation. Ostensibly it is still a blocking force, but Rommel continues to attack, often in excess of orders, and despite supreme logistical challenges manages to suck the British into a larger conflict when it becomes obvious Egypt may seriously be threatened. It must also be stated that strategically it is an absolute opportunity for an isolated Britain: The Germans are providing the British with the opportunity to fight with German ground forces and give the British a much-needed opportunity to fight and defeat the German army in a land engagement.

This is where /u/DBHT14's mentioned concerns come in; had the Axis seized the Suez, the British would have been effectively cut off from their forces in Burma, Australia, New Zealand, India. Worse still, Iraq may have been seriously threatened by Axis attack, and the oil there would have been a complete windfall for fueling Axis advances into the Soviet Union.

Luckily the British forces were expanded at an equally rapid rate, and command shifted to more dynamic individuals. Unlike Rommel, who despite the Italian's best efforts to keep supplied, the British generally attacked only when they were ready and when they had the supplies to sustain an advance.

TL;DR: Africa was an important colonial theater for Italy, whose initial failings during Operation Compass led to German intervention, and a rapid escalation of operations thereafter. Slowly but surely ensuring that battles in the Western Desert, and North Africa in general would end as an overwhelming Allied victory.

Sources: Rommel's North Africa Campaign: September 1940 - November 1942 by Greene, Jack et. Massignani, Alessandro.

Gazala 1942: Rommel's Greatest Victory by Ford, Ken

Tobruk by Carver, Michael