No, it has nothing to do with the "sweet science" of pugilism. And how the sport of boxing was given that moniker is a whole 'nother post. And it's not about returning those unwanted gifts. Boxing Day, which is celebrated in Great Britain and most of the Commonwealth nations on December 26th, apparently got its name from the practice of the gentry giving their servants boxes of celebration leftovers and other small gifts on this day. The servants would have to work on December 25th but would then be given the following day off, along with their presents.
An alternative explanation is that the church alms boxes where parishioners would deposit coins for the poor would be opened on this day and distributed to the destitute of the parish. As years passed, the custom of giving small gifts grew to include anyone who had rendered a service over the course of the year.
December 26th is also the Feast of Saint Stephen, the first Christian martyr. Saint Stephen was one of the seven original deacons of the Christian Church who were ordained by the Apostles to care for widows and the poverty-stricken. For the success of his preaching and his religious devotion, St. Stephen was stoned to death by a mob outside the city of Jerusalem. As he died, he begged God not to punish his killers.
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