What does Boxing Day have to do with boxing?
early 14c., from Old French ambler "walk as a horse does," from Latin ambulare "to walk, to go about, take a walk," perhaps a compound of ambi- "around" (see ambi-) and -ulare, from PIE root *el- "to go" (cf. Greek ale "wandering," alaomai "wander about;" Latvian aluot "go around or astray"). Until 1590s used only of horses or persons on horseback. Related: Ambled; ambling. As a noun, from late 14c.