The short answer is not a whole lot. But for a longer answer I'll give you a overview of each campaign the Italians were involved in.

The invasion of France:

The Italians invaded France after the Germans had. They invaded along their border in the alps. Mussolini only did this so he could have a seat at the impending peace talks. Italy didn't really take any territory and any attacks they launched were pushed back. Italy gained a small portion of France that was later extended when Fall atilla was enacted.

North Africa:

The most famous Italian front and one of the more famous fronts in ww2. The Italians invaded British Egypt and advanced along the coast, eventually stopping to dig in. Seeing that they really couldn't do much against the Germans the British began to focus heavily on Africa, they sent huge amounts of men and resources to North Africa and crushed the Italians (operation compass) this is when The afrika Korps was dispatched to North Africa. After this the Italians fell under the command of the Germans.

East Africa:

The lesser known Africa front. The Italians actually had some victories here. They pushed the British out of Somalia, but this didn't last long and the British counter attacked and kicked the Italians out of east Africa .

Balkans:

The Italians had annexed Albania in 1938 and decided to invade Greece. However, they had not counted on such stiff Greek resistance the Greeks pushed the Italians back to Albania and the Germans were forced to invade to bail out there allies. The Germans had to invade Yugoslavia to get to Greece, the Italians participated in this invasion and were successful but that was mainly because of Germany. The Germans also did most of the work in Greece.

Russia: the Italians sent an army to help the Germans in the Soviet Union. They fought well and earned the respect of the German commanders. But the army was eventually destroyed by the soviets in their encircling of Stalingrad. Not completely destroyed but it really wasn't able to do much in terms of offensive operations after that.

So overall the Italians didn't do a whole lot strategically in ww2. It seems they often got crushed and had to call for German assistance. The Italians tended to be a liability, despite their soldiers being brave and willing to fight.

Sources:

Italian Soldier in North Africa 1941-43 by: Pier Paolo Battistelli

The Second World War: John Keegan

Mussolini: Denis Smith

Inferno: The World at War, 1939-1945: Max Hastings