The Allied success in the North African campaign had at least three important consequences.
First, this was the first land action that the United States was involved in in the European Theater in this war. This was important because it gave the US Army real battlefield experience which it had not had in that theater. This helped allow it to prepare for the more serious battles ahead.
Second, this success led to the invasion of Italy. Without defeating the Axis in Northern Africa, the Allies would not have had a good jumping-off point from which to invade Italy. This allowed the Western Allies to make their first incursions onto the actual continent.
Perhaps the most important impact of the North Africa campaign was to weaken the German military. Once committed to North Africa to help its Italian allies, the Germans had to put significant numbers of forces into the area. This weakened German efforts elsewhere. It also led to the capture or destruction of large numbers of personnel and materiel. All of this made Germany much weaker than it would otherwise have been.