What a word! Well, it's Greek. Of course everybody knows the Latin word for it, manifestation! Appearance, in plain English. It is a time in the Christian Year when we celebrate Jesus as the appearance of "God with us" or the "the Saviour of the World" or "God's Son". Really it is all of these and more.
With the change of the calendar some centuries ago it has meant that Christians from Eastern (Orthodox) traditions have celebrated the sixth of January as Christmas, whilst we Western Christians have a double celebration insofar as we celebrate Christmas on December 24 and then the Epiphany on January 6.
The visit of the Magi is often seen as indicative of the Epiphany, These powerful and influential people came to bring gifts of Gold, Frankincense and Myrhh. These gifts symbolise the person of Jesus the Christ. Gold for a King, Frankincense for prayer, and Myrhh to point to his death. In offering their gifts and their worship they were denying the power of Herod the King and returned home avoiding encountering him again to report the whereabouts of the vulnerable child whose presence inaugerates the reign of God.
Join the celebrations with a bunch of Christians near you, check out a church and push your way in. If the celebrations seem a little traditional or formal don't worry, they have been doing it for 2000+ years. Sit with it a while and get caught up in the mystery.