A ball is a formal party with dancing. In the late nineteenth century, when The Prisoner of Zenda was written, all guests would have been in full evening dress (white tie and tailcoats or full-dress military uniforms for the men, long gowns and elaborate jewelry for the women). Such dances as the waltz and the quadrille (both of which are mentioned) would have been accompanied by an orchestra. There would have been a separate area of the room for champagne and supper.
The ball was arranged by Colonel Sapt. Before the King of Ruritania was drugged and captured, he had shown no particular affection for his cousin, Princess Flavia, whom he was engaged to marry. While the king himself has a mixed reputation, due to his drunkenness and irresponsibility, the princess has always been very popular with the people, and marriage with her would greatly improve the king’s image and strengthen his political position. Her name has recently been linked with that of the king’s half-brother, the Duke of Strelsau, and this has greatly increased the duke’s popularity. Sapt therefore announces that the king will give a ball in honor of Princess Flavia, to increase the king’s popularity and reconfirm their engagement. Sapt wants Rudolf Rassendyll, who is taking the king’s place, to propose to the princess for these political reasons, whereas Rudolf is tempted to do so because, unlike the king, he is in love with her.