According to Wiki & other sources, it was the day the gentry gave their Xmas presents [known by semi-archaic name of 'Xmas boxes'] to their servants, as thanks for their services thru Xmas period.

Nothing to do with fisticuffs, alas, as always used to imagine as a child - esp since cousin of same age & I both received mini-boxing-gloves as Xmas prezzies at age 4 or 5 [1936 or 37] & were first shown rudiments of the noble art by my father & an uncle who had both boxed in student days {which I never really followed up, but cousin boxed 11 or so years later in first team for St Pauls School, which not bad} — hence my semantic confusion for many years: &, judging by name you have given to this thread, yours also!