I like to believe it’s called Boxing Day because it’s the day you put your least favorite present in a box and give it away. I’ve also heard that this is the day to box up leftovers from your Christmas dinner and give them to the poor.
In 19th century England, this was the day employers gave gifts to their servants. Tradesmen, servants and children went “boxing,” going from house to house, soliciting Christmas tips from householders, which they deposited in slitted earthernware Christmas boxes. This poem, quoted by Kightly, seems to reflect this custom:
When Boxing Day comes round againO then I shall have money
I’ll hoard it up and Box and all
I’ll give it to my honey.