The Situation
In 1942, the Second World War had reached a turning point. The Allies were desperate to slow the Germans' eastward advances in Egypt and the Soviet Union. The British were busy battling Erwin Rommel and his Afrika Korps. Stalin was demanding that the western Allies open up a second front in Europe to relieve the pressure on the Red Army. Prime Minister Winston Churchill suggested an invasion of North Africa, followed by an invasion of Europe in 1943. Roosevelt agreed to support his British ally and it was decided that an invasion of North Africa would be staged. The Anglo-American force was to seize Morocco and Algeria, which were controlled by Vichy France, then push eastward to meet the British 8th Army, which was commanded by General Montgomery.
The Invasion
On November 8th, 1942, the Allies landed. A naval task force consisting of five aircraft carriers, three battleships, seven cruisers, 38 destroyers, and various support vessels was dispatched to Morocco to lead the attack. Three attack groups, which numbered 7,000, 19,500, and 9,500, landed at Safi, Fedala, and Mehedia-Port Lyautey. Other landings occurred at Oran and Algiers. They met sporadic but determined Vichy resistance which claimed cost 556 American lives, as well as about 300 British and 700 Free French soldiers. The invasion was a complete success. Despite Hitler's warnings that Vichy France would be invaded if they did not resist the Allied invasion, the French leader in Algiers, Admiral Jean Darlan, agreed to a cease-fire on the 11th. Most French units followed Darlan's lead, but Pétain tried to rescind Darlan's order, and some Vichy soldiers joined German units in Tunisia.
The Aftermath
Darlan was appointed leader of French North Africa by Dwight D. Eisenhower, angering Charles De Gaulle. Darlan would soon be killed by a Free French assassin. After consolidating their strength in French territory, the Allies struck into Tunisia, nearly capturing Tunis before a German counterattack drove them back. In the East, Montgomery drove Rommel's retreating army back to Tunisia and Rommel was replaced by Jürgen von Arnim on March 9, 1943. The two Allied armies, converging on Tunisia, met stiff German resistance, but on May 7 the British took Tunis and by May 13 the Axis forces in Tunisia had surrendered, leaving North Africa under complete Allied control. This paved the way for the Allied invasions of Sicily and Italy, finally opening up the second European front desired by Stalin.
Sources:
http://www.worldwar2database.com/html/torch.htm
http://en.wikipedia.org/wiki/Operation_Torch
Apatrix's excellent node on the Free French