What Role Did The Black Hand Gang Play In Causing The First World War?

Well, they organized and executed the Archduke Franz Ferdinand, which gave the proximate cause for the start of the war. Of course, the long term reasons, such as the alliance systems and militarism of the European countries, were far more important. The Black Hand merely provided the spark to the black powder already present.

World War One started on June 28,1914 when Nedeljko Čabrinović threw a bomb that eventually killed Austria-Hungary's Archduke Franz Ferdinand in which the goal was for Serbia to gain the south-Slav provinces of Austria-Hungary. 

It bounced off the back of the Duke's car and injured 16-20 people with a crater with a 1 ft diameter and a 6.5 inch depth. Austria-Hungary rejected Serbia's offer and subsequently went to war. They both had alliances with other countries globally, Austria-Hungary had an alliance with Prussia (it's "triangular" cross is on the bad airplanes), Germany and the Ottoman Empire and Serbia had Britain, Russia (NOT USSR they dropped out of the war because of the October Revolution), France, and by 1918, America.