Epiphany is the town in which our main characters all live—and it's the town where a lot of peripheral characters, like Noah's grandparents and Margaret Draper, used to live.
It's also the name of the local middle and high schools. Many people just use the word "Epiphany" to refer to Mrs. Olinski's team, especially once victory moves them on to the district competition: Epiphany wins the academic competition, and not just literally.
It's no accident that the novel is set in a town called Epiphany, since an "epiphany" is "a usually sudden manifestation or perception of the essential nature or meaning of something (2): an intuitive grasp of reality through something (as an event) usually simple and striking (3): an illuminating discovery, realization, or disclosure" (source). Check out these moments of epiphany:
All these moments are crucial to The Souls' journeys. At the same time they're working their way toward winning the Academic Bowl, they're also working on even more profound intellectual realizations: What kind of person do I want to be? How do I want to fit into my world? How do I respond with grace to an unkind world?
And there's one more thing. Epiphany is a Christian holiday that falls on January 6th, twelve days after Christmas. In Christian tradition, it's the day that three Wise Men appear to worship the newly born Jesus.
Since many of the characters in The View from Saturday aren't Christian—Julian, Nadia (well, she's half), Noah, and Mr. Singh—Konigsburg probably isn't stressing the religious meanings too much. But, wise men? Given how important "wisdom" is in the novel, you know that's not an accident.