Short answers, pulled from the story.
The Papal States were legally established in 756, when Pepin the Short gave Pope Stephen II lands formerly held by the Lombards, and lasted until 1870, when the Kingdom of Italy annexed Rome. They endured for over a thousand years as a sovereign territory on the Italian peninsula under direct rule of the pope.
At their zenith the Papal States covered most of the modern Italian regions of Lazio, Marche, Umbria, and Romagna, as well as portions of Emilia. They also included the Comtat Venaissin around Avignon in southern France and small enclaves at Benevento and Pontecorvo in southern Italy. In 1649, after the annexation of the Duchy of Castro, the Papal States reached their greatest territorial extent.
The pope gained territorial sovereignty because Byzantine imperial power weakened in the 7th and 8th centuries, leaving the pope as the largest landowner and most prestigious figure in central Italy. Pepin the Short formalized this in 756 by donating to Pope Stephen II the lands formerly constituting the Exarchate of Ravenna after defeating the Lombards.
Rome was captured on the 20th of September 1870 by the Royal Italian Army under General Raffaele Cadorna. The opportunity came when the Franco-Prussian War forced Napoleon III to withdraw his garrison from Rome in July 1870. A plebiscite the following October formally annexed Rome and the remaining Papal States to the Kingdom of Italy.
The Lateran Treaty was signed on the 11th of February 1929 by Benito Mussolini's Italian government and the Holy See. It ended the standoff known as the Prisoner in the Vatican period and created the State of the Vatican City as the sovereign territory of the Holy See, indemnifying the papacy to some degree for its loss of the Papal States.
According to the 1853 census, the Papal States had just over 3.13 million inhabitants, of whom 99.7 percent were Catholic. Jews were the largest non-Catholic group, numbering 9,237 and concentrated mainly in the provinces of Ancona, Ferrara, and Pesaro e Urbino. All other non-Catholic groups combined accounted for only 263 people.