What does Boxing Day have to do with boxing?
Old English half, halb (Mercian), healf (W. Saxon) "side, part," not necessarily of equal division (original sense preserved in behalf), noun, adjective, and adverb all in Old English, from Proto-Germanic *khalbas "something divided" (cf. Old Saxon halba, Old Norse halfr, Old Frisian, Middle Dutch half, German halb, Gothic halbs "half"), perhaps from PIE (s)kel- "to cut."
Used also in Old English phrases as in modern German, to mean "one half unit less than," e.g. þridda healf "two and a half," literally "half third." The construction in two and a half, etc., is first recorded c.1200. Of time, in half past ten, etc., first attested 1750; in Scottish, the half often is prefixed to the following hour, as in German (e.g. halb elf "ten thirty"). To go off half-cocked "speak or act too hastily" (1833) is in allusion to firearms going off prematurely.