Question

How the course of events went from being a local conflict to a world war ?

Answer 1

Answer:   It helped bring a quick victory to the Allies.

The United States had been providing some support to the Allies prior to its own entry into the war.  But when the US joined the effort fully with a declaration of war, that not only meant the arrival of fresh US troops but a commitment of even more American dollars to the Allies' war effort.  The American commitment greatly boosted the morale of British and French troops on the Western front and demoralized the German troops.

As to other answers I've seen suggested with this question in multiple choice format:

• Russia did pull out of the war, but that was because it went through a revolution and change of government in its own country, not because of American involvement.  Russia's fight was with Germany on the Eastern front, whereas the US entered the war on the Western front.
• The United States entered the war on the Western front where the British and French had already been fighting the Germans.
• There were still additional casualties after the Americans entered the war, but bringing the war to an end sooner cut down on the huge losses of life that had been happening.