If you have to be moralistic and are stringed by rules and regulations the whole year, it's only fair to be able let the beast out on one single day a year. At least that's how the clergy reasoned in the late Middle Ages. The day they picked for their debaucheries was New Year's Day, and they called it the Feast of Fools.
The Feast of Fools had its origins in Northern France and was not very widespread. It was a known festival in Britain and England, and was also celebrated in Germany in some cities at the Rhine. The festivities took place on or about January 1st; when a new year was about to begin. The new year was full of questions and uncertainties: will the soil be as fertile as needed, will the harvest be good, will we not lose our sons in battle? The religious festivities of Christmas, a period of fasting and stringent rituals, were just over, and people, not in the least the churchmen, were more than longing to let the beast out.
The nature of the feast was most probably a Christian adaption of the pagan Saturnalia; festivities in honor of the Roman God Saturn, during which social roles were reversed - masters turned to slaves and vice versa. The same inversion of social status was seen in the New Year's festivities of the Middle Ages. A boy from the lower-ranking clergy was elected to be bishop for a day. This Boy Bishop went by several names like "Abbot of Unreason" in France, "Lord of Misrule" in Britain, or "King of the Bean" in England. The latter name derives from the English tradition that the boy who would find the bean that had been hidden in a piece of cake, was to be the King during the festival.
In Paris, the festivities took place in and around the cathedral of Notre Dame in the center of the city. The Boy Bishop held a mock service, in which religious rules and traditions, as well as his superordinates were made fun of. The real bishop and other high-ranked clergymen were relegated to mere spectators. After this phony service, the churchgoers didn't leave the church, but partied, gambled and played at the holy altar. On this day only, gambling for money was permitted - and the people thankfully took advantage of this right. Outside of the cathedral, the Boy Bishop was heading a highly indecent parade. Not minding the January cold (excessive consumption of alcoholic beverages probably kept the people warm), people would display their nudity, sing filthy blessings and dance exuberantly through the streets of the Île de la Cité. Heathenish street plays were performed on the squares, one more offensive than the other. There were no regulations: on this day, people were permitted to do everything that was forbidden during the rest of the year.
This godless behavior, performed by the churchmen in the holy house, was evolving for a thousand years up until the 15th century. By then, the church finally had enough of getting ridiculed and the feast was declared forbidden. Up until three centuries before, popes and bishops had already been protesting against the festivities, but without much effect - in that time, the feast was even spreading out through Germany, Spain and Italy. The feast finally died out in the 16th century.