Epiphany means manifestation. The season of Epiphany is when Jesus began to manifest his power on Earth as the Son of God. He was always the Son, but after his baptism- the power of the Spirit within him became more evident and particularly manifested (became visible) itself in the signs and miracles that Jesus did as he lived among us.
When we say, "I had an epiphany"- we often mean "Things suddenly became clear" or "All the pieces came together for me" or "I found the solution". What had previously been absent was seemingly revealed. Therefore what we usually mean when we use the word "epiphany" is revelation.
Revelation means revealing or unveiling. We have the book of Revelation because John uses the phrase "The Apocalypse of Jesus Christ". Apocalypse comes from a Greek word, apokalypsis, meaning to uncover. A revelation makes clear something that was previously unclear. We are suddenly able to see all the pieces fit together. The reason becomes clear. The solution becomes obvious. The plan is revealed. The end is revealed. (For some of you, the name of Revelation may seem ironic since for many people it seems to be anything but clear.)
A revelation reveals. What it reveals may yet be intangible or still difficult to understand. An epiphany makes tangible something that previously seemed ethereal or unreal. God seemed far away, but the promises of presence were fulfilled and made concrete in Jesus Christ. Hence, Epiphany. The early church (and the current church) struggle with right relationship, balance between right doctrine and right community spirit, and participation in the world- how will this play out, how do these things come together, what will happen- the answers to these questions are revelation(s).