E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A small gratuity given to servants, etc., on Boxing Day (the day after Christmas Day). In the early days of Christianity boxes were placed in churches for promiscuous charities, and opened on Christmas Day. The contents were distributed next day by the priests, and called the dole of the Christmas box, or the box money. It was customary for heads of houses to give small sums of money to their subordinates to put into the box before mass on Christmas Day.
Somewhat later, apprentices carried a box round to their masters customers for small gratuities. The custom since 1836 has been gradually dying out.