What is the origin of boxing day'?

December 26 is called Boxing Day in England and other countries in the Commonwealth, but it is unknown exactly when it first began.

Boxing Day seems to have originated in the mid nineteenth century in England. Some historians believe the name 'Boxing Day' came about because the boxes placed in churches where parishioners deposited alms (coins) for the poor and needy were opened, and the contents were distributed on December 26, which is also the Feast of St Stephen. (St Stephen was the first Christian martyr.)

Others believe that the Boxing Day tradition originated as a holiday for members of the upper class to give boxes containing food, clothing or money to tradespeople and servants, in much the same way that many employers offer their employees bonuses today. These gifts were usually given in boxes; hence the name 'Boxing Day".

Oxford English Dictionary says this comes from the Christmas box; the verb box meaning: To give a Christmas-box, and then leading to the term boxing-day.

An extension of the above theory is that when Christmas holidays were much shorter than they are today certain services often only had Christmas Day as a holiday and returned to work the day after. These included services such as the mail, newspaper or milk delivery. Householders would give them a Christmas gift or, as it was commonly called, a Christmas box on this day to thank them for their service throughout the year.

The common theme, however, is that Boxing Day has absolutely nothing to do with the sport of boxing.

Likewise, it does not gain its name from the overpowering need to rid the house of an excess of wrappings and mountains of now useless cardboard boxes the day after St Nick arrived to turn a perfectly charming and orderly home into a maelstrom of discarded tissue paper.

The name also has nothing to do with returning unwanted gifts to the stores they came from, despite its common association with hauling about boxes on the day after Christmas.
as after Christmas families had extra food left over so they would put it into boxes and bring it around to their neighbours
It was custom for tradesmen to collect boxes of gifts for charities and homeless. Now its just a holiday boxing day dates back to around 400 A.D. but its true origin remains a mystery.