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.

Terms like these are often used by particular writers to mean particular things, but a simple explanation is that verbal irony is saying one thing and meaning another.

I'm not sure where you got that list of "6 types of irony". I've never seen that particular list before, so to the best of my knowledge, it's not a commonly accepted set of types, but something that one particular writer made up to illustrate his point. If that's the case, it may well be useful as a general explanatory tool of the meaning of irony, but I wouldn't get too wrapped up in detailed definitions of each. People are always coming up with lists of "the 6 types of mystery story" or "the 8 kinds of politician" or whatever. To the extent that such categories are useful in understanding the author's point, great. But I wouldn't try to memorize them or agonize over ambiguities, because the next book you read will talk about the 7 types of mystery story and the 3 kinds of politician, and they'll be totally different.

Of course some such lists become well-known and widely accepted, and at that point they have at least literary interest. Like Plato's 6 types of government, the 7 Deadly Sins, etc.