Perhaps because of boxes that were placed outside churches to collect special offerings tied to St. Stephen's Day; or because of the old British custom of tradesmen collecting “Christmas boxes” of money or presents on the first weekday after Christmas as thanks for good service, mentioned by the English diaristSamuel Pepys (1633–1703).[1]
There are plenty of discounted Christmas items in the Boxing Day sale.
1875, Charles Maurice Davies, “Boxing-day on the Streets”, in Mystic London, or, Phases of Occult Life in the Metropolis, London: Tinsley, →OCLC:
Boxing-day in the London streets, and especially a wet Boxing-day, can scarcely fail to afford us some tableaux vivants illustrative of English metropolitan life. […] Christmas-eve of the year about which I write was bright and springlike; Christmas-day dismal, dark, and un-Christmas-like; but Boxing-day that year was essentially muggy, sloppy, drizzly, and nasty.
[1902], On Boxing Day, December 26th, 1902, the Sixth Grand Annual Pantomime, “Jack & the Beanstalk”: With which is Incorporated the Patriotic Legend, “St. George and the Dragon.” (pantomime programme), Kingston upon Thames, London:[Royal County Theatre], →OCLC, title page:
On Boxing day, December 26th, 1902, the sixth grand annual pantomime, "Jack & the beanstalk"
2015 January 5, Steven J. Bennett, “Rule #12: Boxing Day”, in 365 Rules of the New World: If We Had a Chance to Do It All Over Again, Would We Do It Right?, Bloomington, Ind.: Balboa Press, Hay House, →ISBN, page 483:
Think about all those Boxing Day sales, then sit back and relish in the fact that you have enough and that you don't give a shit.
2016 December 22, Chloe Kerr, “More turkey! Where does Boxing Day get its name, what are its origins and how is it celebrated?”, in The Sun, London:
Boxing Day is celebrated on December 26 each year and is a national holiday in the UK. […]Boxing Day is a time to spend with family or friends, particularly those not seen on Christmas Day itself. It is also a day to eat left over turkey. […]Boxing Day is also a time when the Brits show their eccentricity by taking part in all kinds of bizarre traditions including swimming the icy cold English Channel, or running into the sea, fun runs and charity events. December 26 is a big day for sales too. Dramatic price reductions lure out millions of shoppers who even queue for hours before the shops open.
Samuel Pepys (1663 December 19) “19th December 1663”, in Henry B[enjamin] Wheatley, editor, The Diary of Samuel Pepys M.A., F.R.S. Clerk of the Acts and Secretary to the Admiralty: For the First Time Fully Transcribed from the Shorthand Manuscript in the Pepysian Library, Magdalene College, Cambridge, by the Rev. Mynors Bright, M.A., Late Fellow and President of the College, with Lord Braybrooke's Notes, St. Olave edition, volumes VI (July 6, 1663 – Dec. 31, 1663), New York, N.Y.: George E. Croscup, published 1893, →OCLC, page 359: “Thence by coach to my shoemaker's and paid all there, and gave something to the boys' box against Christmas.”