1520s, "act of entering," from Middle French entrance, from entrer (see enter). Sense of "door, gate" first recorded in English 1530s. Meaning "a coming of an actor upon the stage" is from c. 1600.
"to throw into a trance," 1590s, from en- (1) "put in" + trance (n.). Meaning "to delight" also is 1590s. Related: Entranced; entrancing; entrancement.