What does Boxing Day have to do with boxing?
Old English ruh "rough, coarse (of cloth); hairy, shaggy; untrimmed, uncultivated," from West Germanic *rukhwaz "shaggy, hairy, rough" (cf. Middle Dutch ruuch, Dutch ruig, Old High German ruher, German rauh), from Proto-Germanic *rukhaz, from PIE *reue- "to smash, knock down, tear out, dig up" (cf. Sanskrit ruksah "rough;" Latin ruga "wrinkle," ruere "to rush, fall violently, collapse," ruina "a collapse;" Lithuanian raukas "wrinkle," rukti "to shrink").
The original -gh- sound was guttural, as in Scottish loch. Sense of "approximate" is first recorded c.1600. Of places, "riotous, disorderly, characterized by violent action," 1863. Rough draft is from 1690s. Rough-and-ready is from 1810, originally military; rough-and-tumble (1810) is from a style of free-fighting.
late 15c., from rough (adj.). Related: Roughed; roughing. Phrase rough it "submit to hardships" (1768) is originally nautical:
To lie rough; to lie all night in one's clothes: called also roughing it. Likewise to sleep on the bare deck of a ship, when the person is commonly advised to chuse the softest plank. [Grose, "Dictionary of the Vulgar Tongue," 1788]To rough out "shape or plan approximately" is from 1770. To rough up "make rough" is from 1763. To rough (someone) up "beat up, jostle violently" is from 1868. The U.S. football penalty roughing was originally a term from boxing (1866).
c.1200, "broken ground," from rough (adj.). Meaning "a rowdy" is first attested 1837. Specific sense in golf is from 1901. Phrase in the rough "in an unfinished or unprocessed condition" (of timber, etc.) is from 1819.