In order for a balance of power system to work, there need to be a number of states with relatively similar amounts of power. Balance of power cannot occur in a bipolar or unipolar system. If there are a number of similar powers within a system, they can form alliances to oppose any power that looks like it might be moving towards war.
A balance of power system existed in Europe at various times in the past. When this system existed, countries like France, England, Germany, Russia, and Austria were all important powers. In such a situation, let us imagine that a dispute arises between Germany and Russia and Germany is threatening to go to war. In such a case, France and England (for example) could threaten to oppose Germany in case of a war. By balancing Germany's power, they can prevent a dispute between Germany and Russia from escalating into a war.