What does Boxing Day have to do with boxing?
1520s, "act of entering," from Middle French entrance, from entrer (see enter). Sense of "door, gate" first recorded in English 1530s.
"to throw into a trance," 1590s, from en- (1) "put in" + trance (n.). Meaning "to delight" also is 1590s. Related: Entranced; entrancing.