The word epiphany means manifestation, revelation, new insight. On the Solemnity of Epiphany we celebrate the revealing of Christ to the Magi. Epiphany is on the sixth of January, twelve days after Christmas. However, in most dioceses, Epiphany is transferred to the Second Sunday after Christmas (the First Sunday being the Solemnity of the Holy Family). In the East, Epiphany is known as Theophany, a word from Greek for God revealing Himself to humanity. At least these are the notes I have on Epiphany from one of my college theology classes.
The Solemnity of Epiphany celebrates one specific epiphany, one specific revelation of God Himself to the Magi from the East. Epiphany was when Jesus Christ was first revealed to Gentiles, non-Jews. Epiphany is when we remember that Jesus Christ came to save everyone in the world. He came for us so that we might be freed from slavery to sin.
I wish you a wonderful Epiphany!