Many different ideas as to why it was named that.
All the answers below are valid, so maybe it is one, or even all of them.
- A ‘Christmas Box’ in Britain is a name for a Christmas present.
- Boxing Day was traditionally a day off for servants and the day when they received a ‘Christmas Box’ from the master. The servants would also go home on Boxing Day to give ‘Christmas Boxes’ to their families.
- A box to collect money for the poor traditionally and placed in Churches on Christmas day and opened the next day - Boxing Day.
- Great sailing ships when setting sail would have a sealed box containing money on board for good luck. Were the voyage a success, the box was given to a priest, opened at Christmas and the contents given to the poor.