Irony is saying something using wording in a clever way to mean the opposite of the literal meaning of your utterance. Sometimes synonymous with "sarcasm", irony can be subtle or quite crude. If someone drops their cafeteria tray spreading food across half the floor, "That was clever!" would qualify as a rather lame example of irony. Subtle irony might not be noticed for what it is until sometime later (or never, in the case of your average conservative).
Irony can also refer to an event or situation. For example, it would be ironic if an arsonist died in his own fire. This sort of irony can also be termed 'poetic justice.' It is ironic when you throw away that weird tool you've kept for all these years, and the following day you run into a situation where you need to use it. It is ironic when an conservative male evangelical preacher who says all gays will go to hell is caught in bed with a man. Or when a conservative politician who voted against equal rights for gays gets caught soliciting sex in the men's room. Or when it turns out a conservative talk show host is addicted to oxycontin and gets off easy after railing for years against drug abusers and advocating tougher sentences for drug addicts. Or when conservatives dismiss the "collateral" deaths of tens of thousands (or is it hundreds of thousands?) of Iraqis killed as "unavoidable in the noble effort to give Iraqis freedom." During the Vietnam War a similar example of unintentional conservative irony was summed up in the phrase, "we had to destroy the village to save it." In the medical profession the equivalent example of irony is "the operation was a success - but the patient died."