Well, the Vatican City as we know it didn't exist during Garibaldi's time. The Pope ruled the Papal States, but from the Palazzo Quirinale in central Rome rather than from the Vatican. The final Pope to exercise temporal control over the Papal States was Piux IX, and when he came to power, the Papal States stretched from the countryside around Rome, all the way to the region around Bologna and Modena in the north. During the process of Italian Unification, this territory gradually shrunk, and by the time the Kingdom of Italy was declared in 1861, the Pope only exercised power in Rome itself.

Obviously Garibaldi (and the Italian king, Vittorio Emanuele II) were keen to see Rome become the capital of a unified Italy, but Rome was garrisoned by French troops, with the French emperor Napoleon III personally guaranteeing the Pope's protection. Attacking Rome would cause a major international incident, and almost certainly war with France, regarded as one of, it not the, preeminent military powers. As it happened, France's military failed to live up to its reputation during the 1870 Franco-Prussian War, and Napoleon III suffered a crushing personal defeat and capture at Sedan. The French Second Empire fell, and the new Third Republic was in no position to defend Rome. Italian troops assaulted Rome on the 20th September, and Papal troops capitulated after a token resistance. Piux IX retreated to the Apostolic Palace at the Vatican, and declared himself 'prisoner', refusing to recognise the authority of the new Italian state.

Successive Popes considered themselves 'prisoner of the Vatican', and this continued until 1928, when the Lateran Treaty was negotiated by the Italian government under Mussolini. This brought an end to the conflict, with the papacy recognising the Italian state with Rome as it capital. In return, Italy allowed the formation of a state based around the Vatican, and gave it financial support.