It's pretty mysterious. As far as I know the only way we know about this affair is Ovid himself, who only writes about his "carmen et error." People usually assume the carmen was his poetry. What his error was...? He might have been somehow wrapped up in the Julia the Younger scandal (apparently an attempted coup), but no one is sure how exactly.

Here's what he says in Tristia 2:

Though two charges, carmen et error, a poem and an error, ruined me, I must be silent about the second fault: I’m not important enough to re-open your wound, Caesar, it’s more than sufficient you should be troubled once. The first, then: that I’m accused of being a teacher of obscene adultery, by means of a vile poem.

The rest of the poem is a defense of his poetry, basically arguing anything obscene one detects in it they are making up themselves.

He won't talk about the error. We can only guess.