This phrase is mostly commonly found at the end of every broadcast of "The Daily Show", with Jon Stewart saying the tag line after the last commercial break, and throwing up a short video clip before the end credits.
A moment of Zen is something which inspires in the same reaction as does contemplating Zen koans does.
In Zen practice, deliberately irrational statements are sometimes used in Zen to jar persons into realizing the limits of the common uses of the intellect. One well-known example is, “What is the sound of one hand clapping?”.
Either of these instances can be applied to Jon's "moment of Zen", which often depicts political figures making fools of themselves, or satirizing the American public in general, so the epiphany can come from the realization of the satire, or the realization of how some people are just really, really stupid.
"Here it is folks, your moment of Zen!"
(clip appears onscreen of Italian Prime Minister talking about "bunga-bunga" parties, and the news correspondant realizing he means orgies)
The phrase was coined by Ear Training guru Mitch Harpers, who is one of Berklee's textbook writers and a distinguished professor at the renowned music institution.
It's a phrase that can be used as a "positive-negative" name for the school, such as "bad" or "wicked" are used in modern American speech, but most often is used in endearing frustration attributed towards the quirks that come with attending a world-class music conservatory; the reasoning behind the statement is often given by students regarding staff members: "Just because you are a good musician, doesn't mean you are a good administrator".
I can't play for your band this Friday, I have a recording session at Berzerklee that night, sorry.