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.