I really like the season, even though I never seem to have enough energy to devote the energy to it that it deserves. Coming after Advent/Christmas and before Lent, it just seems underrated to me.
The theological term "epiphany" means an "appearance" or "manifestation" and in Christian circles it refers to the manifestation of God in the human Jesus. The Greek term epiphany comes from (attention all my former Greek students!) is epiphaneia and it is a compound verb from the preposition epi (in, on, with, etc. depending on the case it is used with) and phanos (torch or lantern). The verb form means literally to "shine a light on" or "to make visible".
Epiphany also has a secular meaning as a new self-understanding or a revelation of a person's or thing's true essence. Obviously these two meanings are related, and depending on your definition or delineation of sacred vs. secular you could argue the latter has non-theological uses. I would argue that any new self-understanding that is true or for that matter any new and real understanding of the world around one's self is inherently theological. (I realize of course that philosophers will always continue to debate the validity and meanings of "true" and "real".)
Interestingly, on today's Writer's Almanac with Garrison Keillor (broadcast daily on public radio), there is an excellent explanation of both uses of the term epiphany and a concise explanation of how James Joyce used the literary device of epiphany in The Dubliners.
While I was in New York, I became acquainted with the celebration of Three Kings Day in the Hispanic community which is essentially Epiphany but far more elaborate than anything I had known previous. Of course, the account in Matthew makes no mention of the Magi as Kings--for that matter it doesn't even say they were "wise men". However, from the perspective of Matthew, they were obedient and open to the signs of God breaking into our world.