There is no clear consensus about the precise meaning of 'ironic', and there are many different kinds of irony. The key ingredients appear to be incongruity and/or a divergence between apparent and actual meaning – but the word is often used in ways which don't conform to these notions.
The derivation is from the eiron (dissembler), who was one of the stock characters of Greek comedy. He is basically a clever underdog who triumphs over the alazon (braggart) by feigning stupidity – like Peter Falk’s Columbo character, for example.
Examples of different sorts of irony include the following:
The most unambiguous meaning of irony is, 'consisting of, containing, or resembling iron.'
The observation that the situations described in the song 'Ironic' mostly aren’t ironic is commonplace. The main irony associated with the song is that it’s often used as an example of how Americans don’t understand irony – Alanis Morrisette is Canadian.
The name Caesar probably comes from the Latin caesaries, meaning 'a beautiful head of hair'. Caesar was bald.
My mother never saw the irony in calling me a son-of-a-bitch.
John Kendrick was an American sea captain who put into Honolulu Harbour in 1794 and was killed by the cannon which was fired to salute him. The Elves think this is situational and, arguably, comic irony (although it wouldn't have been very comical for Kendrick).
Clement Vallandigham was an Ohio lawyer who died in 1871 whilst defending a man accused of murder during a bar-room brawl. In order to show how the pistol might have gone off accidentally, he grabbed a gun, put it in his pocket, and re-enacted the events as he imagined them. The pistol went off, and Vallandigham died of the wound he received - but not before he had seen his client duly acquitted. This spectacularly successful piece of courtroom theatre is another example of situational irony.
In 1989, convicted murderer Michael Godwin had his sentence reduced to life imprisonment after five years awaiting the electric chair, but was then electrocuted accidentally while sitting naked on a steel toilet seat in his cell in Columbia, SC. Trying to fix his television set, he bit into a wire and was electrocuted – cosmic irony on a grand scale.
Irony is banned from early day motions in parliament.
Charlie Chaplin once entered a 'Charlie Chaplin lookalike contest' and failed to even make the finals, let alone win.
Math was always my bad subject. I couldn't convince my teachers that many of my answers were meant ironically.