What is militarism, and how did it influence the nations of europe prior to world war i?

Militarism is a strong dependence on and support for military means as the way for a nation to protect its interests over against others, and a readiness to pursue military actions aggressively.

Militarism showed itself in a major military buildup and arms race between the nations of Europe prior to World War I.  The militarism increased tensions overall between the nations of Europe.
Along with increasing expenditures on military forces and navies, there was pressure to form alliances with other nations to strengthen a nation's defenses in case there was a war.  The Triple Entente and the Triple Alliance set up in opposition to each other.  This also led to all sorts of war planning on the part of the military generals.  Perhaps the most famous plan was the Schlieffen Plan, named after the German general who proposed it.  Because Russia and France were tied together in an alliance, and opposed to Germany, the Schlieffen Plan determined that a quick strike against France  on the western front would be necessary in order to focus any war efforts against Russia in the east.  This played into the start of World War I, because when only Germany (along with Austria) and Russia were involved in war declarations after the assassination of Austria's archduke Franz Ferdinand, the first thing the German army did was to go and attack France.  
The nations and their militaries were preparing for war, ready for war ... and when there was an excuse for war, they all charged quickly into war.