In addition to the great examples that were given in the other responses, I just wanted to say that as a New Yorker from the younger generation, this is actually a common slang term. I don't know where you heard this, but many young New Yorkers say "she went off on him," for example, to say that they got very angry and started to yell at the other person. So when I first read this, that was actually the first meaning that came to my head, although it is very coloquial and informal. Maybe that helps and/or is interesting for you!