What does Boxing Day have to do with boxing?
1560s, from French druide, from Latin druidae (plural), from Gaulish Druides, from Old Celtic *derwijes, probably representing Old Celtic derwos "true" and *dru- "tree" (especially oak) + *wid- "to know" (cf. vision). Hence, literally, perhaps, "they who know the oak" (perhaps in allusion to divination from mistletoe). Anglo-Saxon, too, used identical words to mean "tree" and "truth" (treow).
The English form comes via Latin, not immediately from Celtic. The Old Irish form was drui (dative and accusative druid; plural druad); Modern Irish and Gaelic draoi, genitive druadh "magician, sorcerer." Not to be confused with United Ancient Order of Druids, secret benefit society founded in London 1781.