Italy was a pre-War European country. By 2060, as the European Commonwealth dissolved, the country fell into disarray, bickering and quarreling with its neighbors over the last few remaining resources on Earth.
Italy is the headquarters of the renowned firearms manufacturer Beretta.
Aside from the appearance of the reversed Italian flag on Colontoni's Pizzeria in Point Lookout and the appearance of Beretta weapons in Fallout Tactics and Fallout: Brotherhood of Steel, there are no mentions of Italy in the published Fallout games.
The plot of J.E. Sawyer's hypothetical Fallout: Resource Wars game would involve a crew of soldiers from the Royal Armoured Corps who become stranded in a war-torn anarchistic northern Italy and have to fight their way to the English Channel in a bunch of quickly degrading vehicles, scavenging replacements, fuel, and weapons as they go.