Learn English – What exactly is “verbal irony”

My daughter has been given the task – by me – of explaining irony. She identified and did a jolly good job of explaining 5 of the 6 apparent types of irony: dramatic, cosmic, socratic, situational, verbal, and irony of fate.

When it came to verbal irony she (we) stumbled. She is happy to accept that verbal irony is equivalent to sarcasm, but I would appreciate confirmation of this from the experts in this forum in order that I do not mislead her by accepting her appraisal of the matter.

Just to be clear, I am not asking whether irony is the same as sarcasm in the general case.

What exactly is "verbal irony"?

Update: my daughter's take-away from the answers so far (2012-04-16) is the following — in her own words:

"Verbal irony is when someone says something but means the complete
opposite. Like one person might say, 'Oh, that looks wonderful', in a
kind of giggly voice. Its a bit like sarcasm except it's not negative"

I will accept the answer that get the most votes over the course of the next couple of days. Each point of view expressed has been helpful in its own way and I cannot pick an answer right at the moment, so will defer to the popular vote in the spirit of these sites.