The alliance systems that were formed between various countries in Europe before World War I were not really instrumental in causing the war to break out. However, once it did break out, they were instrumental in making the war spread. In other words, without the alliances, the war might simply have been a local conflict between Serbia and Austria-Hungary, not a world war.
In the years before WWI, alliances arose between many European countries. Germany was looking to increase its strength and was building its military. This alarmed the British, the French, and the Russians. They formed an alliance that they felt would help to protect them from a more powerful Germany. At the same time, the Russians had an alliance with the Serbs. This alliance was based largely on ethnic ties as they were both Slavic peoples. In turn, Germany had an alliance with Austria-Hungary. This was based partly on ethnicity as well.
This set the stage for the conflict between Austria and Serbia to become a world war. When Austria declared war on Serbia, that brought Russia in. Russian involvement led to German involvement on Austria’s behalf. The French and English came in because of their alliances. In these ways, alliances caused the war to become much bigger than it might otherwise have been,