The bishop would symbolically stand down at the moment in the Magnificat when the choir saing deposuit potentes de sede (He puts down the mighty from their thrones). Then the 'boy bishop' would ascend the throne at the words et exaltavit humiles. Apart from the celebration of Mass and the important Vespers and Lauds of Christmas itself, the boy would officiate at many services and make decrees as to the obligations of the other choristers (usually, extra food, less work, etc.)
It was a popular custom. Eton College elected two boy bishops each year, and all the Cathedrals had them, including St Paul's. The boy's reign would come to an end on Holy Innocent's Day, after he had himself preached a sermon at Mass. His fellow scholars would then have to give him a penny as a Christmas offering.
Like many similar traditions in the Middle Ages and the Renaissance, it served to teach children about the dignity of high office (and especially the importance of the bishop's role in the Church.) It also demonstrates to those in authority the fragility of honour and rank; a warning that they should not cling to earthly honours.
In our pictures here, Bishop Cansick (normally a pupil in year 8) begins his procession before presiding at Pontifical Vespers; and afterwards recieves the customary reverences from pupils and visitors at the end of the ceremony.
Bishop Cansick's symbolic reign only lasted a day, but he made good use of it. Having discharged his liturgical duties with great dignity, he presided at dinner, where he pronounced the blessing and grace. He afterwards decreed a later bedtime and a film evening for all pupils, while the suitably humiliated Chaplain and Masters cleaned the tables and swept the floor.
UPDATE See also: www.chavagnes.org/news for coverage of the Boy Bishops of 2004,2005 and 2006. In our Christmas newsletters on that page you will find articles on the theme.