Boxing Day has nothing to do with the sport of boxing.
Christmas presents in Britain are sometimes referred to as Christmas bosses. Although the official origin of Boxing Day has never been determined, there are numerous theories. A common explanation is it was the day the lord of the manor gave Christmas boxes to the staff who worked serving the festivities of Christmas day. It also can be simply a year-end bonus. Or a token of thanks given to tradesmen.
Nowadays Boxing Day is the day when post-Christmas sales begin: