What does Boxing Day have to do with boxing?
late 14c., castigacioun, from Latin castigationem (nominative castigatio) "a correcting, reproof, chastizing," noun of action from past participle stem of castigare (see castigate).
c.1600, from Latin castigatus, past participle of castigare "to correct, set right; purify; chastise, punish," from castus "pure" (see caste) + agere "to do" (see act (n.)). The notion behind the word is "make someone pure by correcting or reproving him."
If thou didst put this soure cold habit on To castigate thy pride, 'twere well. [Shakespeare, "Timon" IV.iii (1607)]Related: Castigated; castigating; castigator; castigatory.