Originally WWI would have been a small war, but because of the alliance system it compelled other (greater nations) to get involved. Think of it like this, you and I get into a fight and my friends jump in to help me while your friends jump in to help you. This is similar to the alliance system because what could have been a small fight between the two of us becomes something that consists and effects more people than necessary.
if one country got in a conflict with an enemy, that country's allies would have to back that country up. Then the enemy's allies would have to get involved and so on, starting a major war with many countries.