What does Boxing Day have to do with boxing?
Old English brand, brond "fire, flame; firebrand, piece of burning wood, torch," and (poetic) "sword," from Proto-Germanic *brandaz (cf. Old Norse brandr, Old High German brant, Old Frisian brond "firebrand, blade of a sword," German brand "fire"), from root *bran-/*bren- (see burn (v.)). Meaning "identifying mark made by a hot iron" (1550s) broadened by 1827 to "a particular make of goods." Brand name is from 1922.
c.1400, "to brand, cauterize; stigmatize," originally of criminal marks or cauterized wounds, from brand (n.). As a means of marking property, 1580s; figuratively from c.1600, often in a bad sense, with the criminal marking in mind. Related: Branded; branding.