The underlying attitudes which led to the outcomes of the Congress of Vienna were the ideas presented mainly by Metternich at the Congress, and by Edmund Burke years earlier. They were reacting to 25 years of continuous violence (10 years of French Revolution and 15 years of Napoleon). The attitude was never again can we allow so many people to die, either in mass executions at home (the Revolution), or in battle in foreign countries (Napoleon). In order to prevent this, they had to combat the attitudes which led to the Revolution, and those attitudes were the attitudes which Metternich and Burke opposed in their writings. The Revolutionaries said that you had to work for a perfect society, but Burke and Metternich said that perfection was impossible in this life, that you should settle for 99%, and perfection will come in the next life. The Revolutionaries said that you should make sudden radical changes, Burke and Metternich said that you had to respect tradition, because it represents the accumulated wisdom of human reason and human experience, so be slow and cautious when making changes. In practical terms, then, this meant that the Congress of Vienna wanted to make stable legitimate governments which might change slowly over time to adapt to new circumstances, but which would not make sudden revolutionary changes.
Reacting to the Congress of Vienna, there were those eventually came to disagree with it: J.S. Mill and Liberal movement of the 1800's who wanted free markets; the Nationalists who wanted the people of each nation to be free to express their collective identity and not be restrained by traditional governmental structures; and the Communist/Socialists, who thought that the changes and problems inflicted on society by urbanization and the industrial revolution required different political approaches.
So the Congress of Vienna is important, not only because it solved a specific set of diplomatic problems and preserved peace, but also because it symbolizes an outlook: the ideas, philosophies, views, opinions, and goals of Metternich and Burke, of a Europe tired of the bloodshed and mass murder which arose from the French Revolution and from Napoleon. Their plan was to stabilize Europe by restoring the legitimate governments, and by balancing the power among England, Russia, Prussia, Austria, and France, so that none would exercise hegemony over the others.
Equally historic are the movements which emerged, in part, as reactions against the Congress of Vienna: nationalism, J.S. Mill's liberalism, socialism/communism etc.
Liberals were freemarket people back then; nationalists viewed the identity of the nation as coming from the people, not the monarchs, but the Congress of Vienna supported the monarchs.