Short answers, pulled from the story.
A Prince-elector was a member of the Electoral College of the Holy Roman Empire, the small group of princes who chose the Holy Roman Emperor. The office existed informally from the 13th century and was formally codified by the Golden Bull of 1356. The dignity was abolished in 1806 when the empire dissolved.
The original college established by the Golden Bull of 1356 had seven electors: the Archbishops of Mainz, Trier, and Cologne, plus the King of Bohemia, the Count Palatine of the Rhine, the Duke of Saxony, and the Margrave of Brandenburg. The number grew over the centuries, reaching ten electors in 1803 before the empire ended in 1806.
The Golden Bull of 1356 was the constitutional document that formally defined the Electoral College, named the seven electors, and established rules for elections and elector privileges. It granted electors the Privilegium de non appellando, which barred their subjects from appealing to higher imperial courts. The Bull resolved long-standing disputes over who held the right to elect the emperor.
Frankfurt served as the regular site of elections from the 14th century onward. Elections were also held at Cologne in 1531, Regensburg in 1575 and 1636, and Augsburg in 1653 and 1690. In Frankfurt, voting took place in a dedicated electoral chapel called the Wahlkapelle inside the cathedral.
After the empire was abolished in August 1806, most former electors took new titles. The Electors of Bavaria, Wurttemberg, and Saxony became kings; the Electors of Baden, Regensburg, and Wurzburg became grand dukes. The Elector of Hesse-Kassel refused a higher title and kept the now-meaningless rank of Elector until 1866, when Hesse-Kassel was absorbed into Prussia after the Austro-Prussian War.
A Wahlkapitulation, or electoral capitulation, was a contract drafted by the electors from the 16th century onward and presented to a king-elect before he took office. The candidate agreed to concede specified rights and powers to the electors and other princes. Only after swearing to abide by it did the candidate formally become King of the Romans.