It would be untrue to say that “ironically, I don’t understand what irony means”. Not that I understood the understood the nuances behind irony (until recently), but that the sentence itself wouldn’t be an example of irony. If all this is too meta too soon, I’ll back up a bit.
I’ve become aware that many Americans misunderstood the meaning of “irony”, equating it with a gap between what is expected and what actually happens, such as saying “ironically, I encountered a traffic jam when I was already late”. I hesitated in using the word until recently as I didn’t want to contribute to that blunder. A trip to Wikipedia has helped clear up the nature of irony, though.
At first, I skimmed through the article, but that only made me more confused. After reading it more carefully, though, a tidbit towards the beginning helped shed some light on it — “A common metaphor for using irony is to ‘have your tongue in cheek.’”. And, an example that they give is that saying “Lovely weather outside!” — when it's actually raining — would be irony.
So, is irony the same thing as sarcasm, then, you might ask? Well, as I understand it, sarcasm is a subset of irony, with the addition that sarcasm also includes an aspect of ridicule. Anyway, I’m obviously a master of irony now. (See? That’s irony in action ;). )