How did the alliance systems lead to the Bosnian crisis?
The Alliance System was a series of treaties (alliances) at the end of the 19th century and the early part of the 20th century between European Great Power countries. They essentially set up the powerful nations of Europe as groups of friendly entities who had to support each other in the case of dispute or war.
The major alliances were:
The Triple Alliance between Germany, Austria-Hungary and Italy, signed in 1882.
The Entente Cordiale between Britain and France, signed in 1904.
The Anglo-Russian Convention between Britain and Russia, signed in 1907.
In 1908, Austria-Hungary stated its intention to annex Bosnia and Herzegovina. This upset the balance of power that had been established by the Alliance System because Serbia and Montenegro were the neighbors of Bosnia and Herzegovina and laid claim to the area, while nearby Italy wanted compensation as well. Russia historically supported Serbia, due to shared Slavic culture, but its defeat in 1905 in the Russo-Japanese War left Russia unable to lend any clout against Austria-Hungary.
The political crisis ended in 1909 through diplomacy in a seeming victory for Austria-Hungary, but in effect it increased tensions between Austria-Hungary, Serbia, Italy and Russia. This meant that Britain and France also had to take sides.
Prior to World War I, due to these alliances, Europe had basically fallen into two "armed camps" with the allied nations of Germany, Austria-Hungary and Italy in the central part of Europe pitted against Britain and France to their west and Russia to their east. The Alliance System drew lines that would lead to a complete breakdown in diplomacy and the outbreak of World War I in the summer of 1914.
In short, rather than preventing conflict, the Alliance System was a root cause of the Bosnian Crisis and later of World War I.