Question

By June 1943, the allies had regained control of North Africa. What was the advantage of controlling this region?

Answer 1

The British had been fighting Italian and German forces since 1940 and the Americans did not arrive until Operation Torch in November 1942 when they were given a good beating by the Germans at the Kasserine Pass in Tunisia and had to be rescued by battle hardened British and Free French forces. 
North Africa was the key to controlling the Mediterranean and therefore Southern Europe 
It was also the route to the Suez Canal which gave access to the Indian Ocean and would have enabled German forces to link up with the Japanese. 
A British defeat in North Africa would have handed the Axis control of the vast oil reserves of the Middle East ( the Axis was always short of oil) and enabled them to open up a Southern Front against Russia by going through Iran. 
This may have reversed the result of the Battle of Stalingrad.