After the defeat of Napoleon, the European leaders converged at Vienna to discuss ways in which peace would be maintained throughout Europe for years to come. During these discussions, Metternich played an influential role by advocating for the conservatism philosophy as opposed to liberalism and revolutions which he blamed for instability and conflict.
He also held an aristocratic view that kings were supposed to lead the people and as such proposed that the monarchies established before Napoleon’s reign be restored. This led to the formation of the “Holy Alliance” comprising of monarchies from France, Russia, Austria and Prussia. These monarchies would then be guided by a balance of power that provided checks to ensure that none of the countries could overpower the others individually. Also, Metternich while at Vienna founded a system to conduct periodic congresses during which the monarchies would assemble and discuss mechanisms of containing revolution. The establishment of this system in a bid to maintain peace in Europe through balancing power is what is referred to as The Concert of Europe.
At the Congress of Vienna, von Metternich claimed to be basing his actions on the idea of keeping legitimate government in place. He claimed to be favoring monarchs who had "legitimate" claims to their realms. In reality, he was being more pragmatic and working for a balance of power.
What this meant is that Metternich and others tried to have many countries with relatively equal amounts of power. That way, they would cancel one another out and prevent any one country from becoming too ambitious. This was seen as a way to prevent further wars. This system of balanced powers came to be known as the Concert of Europe.