Irony is the use of words in a way to conceal true intention with literal intention. More clearly, irony is when you say one thing but mean another. Much subtext, many puns, and quite a bit of sarcasm and slander are dependant on irony.
When someone gets a new awful haircut and asks you what you think, and you say that it's "a real good 'do" (using "do" to mean she was done over, ie didn't get her money's worth,) you've used irony - whether or not it's obvious probably determines whether you get yelled at.
Similarly, if a plot involves a famous person with a dirty secret, and the famous person asks another character if a third person knows who they are, then a response "Oh, she knows exactly who you are" to answer what the famous person would want to hear but really to mean "she and I know your secret and you're not fooling us" would be the use of irony