Well, I suppose when they say World War, they really do mean the entire world. The Aleutian Island Campaign was a conflict for the Aleutian Islands, which were a part of the Alaska Territory.
A small Japanese force managed to take over the islands of Attu and Kiska but the extreme remoteness and weather of both islands made it hard to hold on to them. It took nearly a year for a larger US force to eject them.
As you can guess by the presence of its story on this site, the conflict is also known as the “Forgotten Battle.” It was overshadowed by the simultaneous Guadalcanal Campaign. There are two major theories in respect to the intent of the Japanese.
Some historians believe that the attacks were diversions to draw out the US Pacific Fleet from Pearl Harbour, while others have argued that that the invasion was meant to protect the northern flank of the Japanese empire.