E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
The time of appearance, meaning the period when the star appeared to the wise men of the East. The 6th January is the Feast of the Epiphany.
The word is not special to Christianity. One of the names of Zeus was Epphanes (the manifest one), and festivals in his honour were called Epiphanies. (Greek, epi-phaino, to shine upon, to be manifest [in creation].)