When used to refer to an event, it means contrary to what's expected, in a striking or poignant or tragic way. It derives from a Greek word meaning "to lie" or "to be insincere." Here's an example of irony: "The speaker, who was famous for his command of the English language, clearly didn't know the difference between ironically and coincidentally." People do often confuse those two words. Here's an example of coincidence, with nothing ironic about it: "The speaker had a third cousin named Hepzibah. So did the man who introduced him." There's nothing about this coincidence that is strikingly contrary to what you expect, so it's not ironic.
(Will be published in the March 2010 issue of Denver's Community News.)
I'm collecting all of these (but I’m way behind) at: