The Italian surrender to the Allies did not have that much of an effect on the war. The Germans held all the defensive positions in Italy anyway and they were the major problem for the Allies even before the Italians surrendered.
The invasion was significant mostly for the following reasons:
- It was practice for the D-Day landings, which would be much more important.
- It boosted morale in the military and at home -- we were doing something to push the enemy back.
- It opened a second front on the continent of Europe to help take some pressure off the USSR, which had been the only country left fighting Germany (on the ground) since 1940.
I believe the question relates to invasion of Italy by Allied forces during World War II.
Axis planes based at Sicily bombed Allied ships in the Mediterranean, Therefore they wanted to capture Sicily to make the Mediterranean safe for their ships and to possibly force Italy out of the war. With this objective Allied forces landed along Sicily's south coast on July 10, 1943. They engaged in bitter fighting with German troops over rugged terrain for 39 days forcing last Germans to leave Sicily on August 17, 1943.
In the meantime fell from power on July 25, 1943. Perhaps fall of Sicily contributed substantially to his fall. Finally Italy surrendered on September 3, 1943.
However, Germany was determined to fight the Allies for control of Italy. To counter the Germans, Allied forces landed at Salerno, Italy, on Sept. 9, 1943. this was preceded by another Allied force landing farther south. The German Positions in Italy were well defended and Allies forces had to struggle in a series of head-on assaults on them. Thus progress of allied forces was slow, but by early November, they nearly reached Cassino, about 120 kilometres south of Rome.
In January 1944, the Allies landed troops at Anzio, west of Cassino, to attempt an attack from behind. However, it took them four months and sacrifice of thousands of Allied soldiers to break through German defences. Finally Rome fell on June 4. Still the Germans held their positions in northern Italy for a long period, and it was only in May 2, 1945, that German forces in Italy finally surrendered.
The main impact of all these evens on war was to secure Mediterranean sea secure for allied forces, and engaging part of Axis forces in defense of Italy. In a way fall of Mussolini also prevented Italy from collaborating with Germany. surrender of Italy to allied forces was a blow to the German morale.