Why exactly did Giuseppe Garibaldi/Mazzini, Victor Emmanuel II, etc. lead a revolution in Italy back in the 19th century?
There was a convergence of a number of factors in the nineteenth century that allowed unification to come to pass in the Italian peninsula.
Firstly, the Napoleonic experience had popularized both the notions of national unity. Although Napoleon's reorganization of the Italy was predicated upon subordinating Italian to French interests, it gave the peninsula something approaching a unified administration. Counter-intuitively, both experience within the French administration and resistance to French rule provided a charter generation for Italian nationalism. Although the governments of Restoration Italy were decidedly against nationalism and other ideological imports from the French Revolution, the national idea percolated through Italian secret societies and emigres.
The result of the Italian states' reactionary attitude was a stalemate between the revolutionary nationalist forces led by the Mazzini/Garibaldi clique and the Italian conservative governments. By the mid-nineteenth century both sides were clearly frustrated with this state of affairs. There's a wonderful Italian word, campanilismo (love/loyalty to one's bell tower- i.e. hometown), which encapsulated the frustration of nationalists. Both Mazzini and Garibaldi hoped that their calls for unification would lead to the Italian masses abandoning their princes and joining a republic. On the state side of the equation, a few adept officials, the foremost among them Cavour, recognized that an alliance with nationalism would benefit and preserve the old order longer than simply reacting against the conspiracies and invasions orchestrated by the nationalists.
The mid-century geopolitical situation allowed for these two camps to merge together despite being at loggerheads since 1815. Louis Napoleon thought he could pose as the champion of the national idea and thus cover the second French empire with glory. Cavour realized that an alliance with the French and the nationalists would strengthen the Kingdom of Piedmont-Sardinia. When Napoleon III realized that Italian unification ran counter to French interests, he reversed course and Cavour's successor, Ricasoli, hitched his star to Prussia.
Neither the nationalists nor the new Italian monarchy was very fond of this arrangement. Victor Emmanuel II was not really prepared to rule as a constitutional monarch but recognized that he would have increased powers as King of Italy rather than just Piedmont-Savoy. The liberal-orientated nationalists stomached an alliance with the monarchy because it was the best route towards a quick and relatively painless unification. Their hope was that after a few generations of parliamentary experience and unification, the new Italian state would create the Italian national identity that they spent fifty years trying to create.
Sources
Beales, Derek Edward Dawson. The Risorgimento and the Unification of Italy. London: Allen and Unwin, 1971.
Mack Smith, Denis. Cavour. New York: Knopf, 1985.
_.Mazzini. New Haven: Yale University Press, 1994.