Happy Epiphany! The Christian tradition of identifying January 6th as the feast day of "Epiphany" (Greek epiphánia) goes back to the fourth century A.D., the same century in which December 25th was settled upon as the date for the Feast of the Nativity, i.e., Christmas. Traditionally, Epiphany commemorates the coming of the Magi to worship the infant Christ. Of course, we also use the word epiphany to mean a sudden understanding or flash of insight: "I just had an epiphany!" means "I just realized something!" So what do these two things—the Adoration of the Magi and sudden realizations—have to do with one another? Why is the word epiphany used for both?
The Greek verb epiphaínō had several related meanings, including "reveal," "show," "display," "manifest"; but its ultimate and original meaning was "to shine upon," "to shed light on." The connection here is pretty clear: when you shed light on something, you make it visible. You show or reveal something by illuminating it, bringing it into the light.
The Christian "capital-E" Epiphany refers, therefore, to the revelation or manifestation of Jesus as the prophesied King, the Messiah. The Magi recognize him for who he is; and they fall down and worship him (Matthew 2:11).
But traditionally, the significance of the Epiphany was not just the fact that Jesus was revealed to be the True King, but rather, to whom this was revealed. The Magi, of course, were Gentiles. They were not part of the Covenant between God and the people of Israel. The great significance of the Epiphany is that it marks the first time God reveals the Messiah, the Savior, to the Gentiles; it is the first indicator that God's Covenant is soon going to be opened up to all the nations. This is gospel—good news—indeed!
The connections between Epiphany as both "revelation" and "light" and the beginning of the New Covenant also makes us think of the words of the "righteous and devout" Simeon, who, upon taking up the infant Christ in his arms, "blessed God" and said "my eyes have seen your salvation...a light for revelation to the Gentiles, and for glory to your people Israel" (Luke 2:28-32). And, of course, our Savior himself declared "I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life" (John 8:12).
As for the "small-e" epiphany, saying "I've just had an epiphany," meaning a sudden insight or realization, is essentially just the Greek way of saying "a light bulb went off in my head." The metaphor is the same: sudden burst of light = sudden understanding.
It's interesting to note, however, that in English the "capital-e Epiphany," meaning the revelation of Christ to the Magi, is much older than "small-e epiphany." The use of Epiphany in the specifically Christian sense is first attested in a lyric from around 1310: one couplet in the lyric runsThe thridde joie of that levedy / That men clepeth the Epyphany, i.e., "The third joy of that lady [Mary] / Which men call the Epiphany." (In 1410 we find an author explaining the definition of "Epyphanye" as "the open shewynge of oure lorde Jhesus.")
But not until over 500 years later do we find the word epiphany being used to mean "a sudden realization." This usage of the word is first attested in the 1840s. (Given that English has somewhat over thirteen-hundred years of recorded usage, something from the 1840s is downright recent!)
Bonus etymology: Does it sound a bit weak, or like an understatement, to describe the coming of the Magi as "the Adoration of the Magi"? Don't we use the verb adore to just indicate a strong liking for something ("I adore chocolate"; "I adore this song"; etc.)? But the Magi didn't just strongly like Jesus; they fell down and worshipped Jesus and gave him rare and expensive gifts!
The explanation is this: it wasn't originally an understatement. The word adore has gone down in significance over the years: Latin adōrō meant "to worship," and that was the original meaning of the word in English as well. (This is the intended meaning of the word in the hymn "O Come All Ye Faithful": the refrain O come let us adore him means "O come let us worship him.")
Wishing you all a blessed and illuminating Epiphany!