What does Boxing Day have to do with boxing?
1620s, "convenient sea room" (both for ships and sailors), of uncertain origin, probably from bear (v.) + abstract noun suffix -th (2) as in strength, health, etc. Original sense is preserved in phrase to give (something or someone) wide berth. Meaning "place on a ship to stow chests, room for sailors" is from 1706; extended to non-nautical situations by 1778.
1660s, of ships, from berth (n.). Of persons (intransitive), from 1886. Related: Berthed; berthing.
A job, appointment, situation, etc: Dissatisfied with his prewar truck-driving berth (late 1700s+ Nautical)