A televised public apology admitting one's fault. Based upon the Latin phrase "mea culpa", which basically means "my bad".
A media culpa is a popular activity for athletes and politicians. Famous media culpas: Bill Clinton, Tiger Woods, David Letterman, Eliot Spitzer, Kobe Bryant, Mel Gibson, Alex Rodriquez, Michael Phelps, Alec Baldwin, Hugh Grant, Michael Richards, Marion Jones, David Hasselhoff, Duane "Dog" Chapman, and on and on and on...
> Did you catch Tiger Woods' media culpa this morning?
> Oh yeah, I've already tweeted upon it thrice.