What does Boxing Day have to do with boxing?
1610s, "word of honor," especially "promise by a prisoner of war not to escape," from French parole "word, speech" (in parole d'honneur "word of honor") from Vulgar Latin *paraula "speech, discourse," from Latin parabola (see parable). Sense of "conditional release of a prisoner before full term" is first attested 1908 in criminal slang.
1716, from parole (n.). Originally it was what the prisoner did ("pledge"); its transitive meaning "put on parole" is first attested 1782. Related: Paroled; paroling.