This is not the primary meaning of the word. The word indicates a great day when the magi showed up on Jesus' doorstep and gave Him gifts. It was the coming of Messiah not just to the Jews (that was earlier through Jesus' family and through the shepherds), but to the Gentiles as well, maybe some pagan royal advisors of some kind from Persia. Suddenly, though, people from other parts of the world were aware of Jesus' coming and were taking the message of this amazing child to others in other lands.
Epiphany is also the day we observe today, celebrating that event. Of all the holidays, this may be the most missionary holiday we have. It is a clear indication of the gospel going to other lands, taken by believing people who were from those lands.
I try to imagine what was happening in the hearts and minds of these men as they presented their gifts. What did they see in the Christ Child as they worshiped? What transformative event could it have been? Did they come in doubt or in faith? Did faith happen suddenly on the spot as we would interpret the word "epiphany"?
May I come to Jesus in faith today, finding as I arrive a Divine human bringing me life and light. May those virtues engulf my spirit like a torrent and wash me anew with His goodness.