What does Boxing Day have to do with boxing?
Old English fyllan "fill up, replenish, satisfy," from Proto-Germanic *fullijan (cf. Old Saxon fulljan, Old Norse fylla, Old Frisian fella, Dutch vullen, German füllen "to fill"), a derivative of adj. *fullaz "full" (see full (adj.)). Related: Filled.
To fill the bill (1882) originally was U.S. theatrical slang, in reference to a star whose name would be the only one on a show's poster. To fill out "write in required matter" is recorded from 1880. Fill-in "substitute" (n.) is from 1918.
"a full supply," mid-13c., fille, from Old English fylle, from Proto-Germanic *fullin- (cf. Old High German fulli, German Fülle, Old Norse fyllr), noun of state from *fullaz "full" (see full (adj.)). Meaning "extra material in music" is from 1934.
To substitute; replace temporarily: I'll fill in for you (1940s+)