What does Prospero stage in order to celebrate the betrothal of Miranda and Ferdinand?

A masque. These were pompous and rather static entertainments which were popular at the time. In including one in the play, Shakespeare was bowing to the popular taste for spectacle. Such spectacular scenes were a feature of his late plays: in A Winter's Tale a real bear appears on the stage, in Cymbeline an actor representing Jupiter is lowered from the stage ceiling for no good dramatic reason, and Henry VIII is full of long and spectacular processions.