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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 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.

Partially taken from "http://wiki.answers.com/Q/Why_is_Boxing_Day_called_Boxing_Day"