Irony, in general, is a contrast between what is stated and what is meant, or between what is expected to happen and what actually happens.

In particular, dramatic irony involves a contradiction between what a character thinks and what the audience or reader knows to be true.

This type of irony occurs frequently in theatrical productions and in cinematic productions. One very simple form of dramatic irony is used in the horror film industry. This is often exemplified as a young, naive woman walks down a hallway or onto a dimly lit path of some kind where the audience knows that the monstrous creature or maniacal killer hides and waits for her. 

In classical works and in modern theatrical productions, dramatic irony is frequently employed. In The Odyssey, for instance, there is dramatic irony in the scene that takes place in the swineherd's hut because Telemachus and Eumaeus do not know that the beggar is really Odysseus in disguise, but the audience does know.

In another example, there is dramatic irony in Shakespeare's Macbeth early in the play. When the second witch addresses Macbeth, "All hail, Macbeth, hail to thee, Thane of Cawdor!" (1.3.50) Macbeth ponders,

....I know I am thane of Glamis;
But how of Cawdor? the thane of Cawdor lives,
A prosperous gentleman...(1.3.72-74)

But the audience knows that King Duncan has earlier ordered the death of the Thane of Cawdor because in Scene 2 he was found to be a traitor.

No more that thane of Cawdor shall deceive
Our bosom interest: go pronounce his present death,
And with his former title greet Macbeth (1.2.63-65)

The general term "irony" means a contrast between two things. Two kinds of irony include irony of situation and verbal irony. Irony of situation is a contrast between what is expected and what happens. For example, a consistent cheater gets cheated on. Verbal irony is a contrast between what is said and what is meant, as in a student who says "I just looooove getting up early to go to school." Of course we can tell that what he meant is nothing like what he said.

Dramatic irony is a contrast between what a character knows and what we (the readers or audience) know.

The words and actions of the characters therefore take on a different meaning for the audience or reader than they have for the play’s characters. 

Cartoons are full of dramatic irony. For example, think about a guy who has his hands full of packages; he is walking along and there is a banana peel lying right on the sidewalk ahead of him. We know what's going to happen next, but he does not. That is dramatic irony, and that is funny. His impending painful fall amuses us even more because we know what is going to happen and he does not. It would be even better if this guy were assuring his wife that he would not fall just as he falls.

A more serious and literary example is when Oedipus curses whoever is responsible for bring a curse on his city; he also curses anyone who has let that person stay in his house, even unknowingly. What we, the readers and audience, know is that he is the one who has done these things and he is actually cursing himself. This knowledge adds to our appreciation for the work. Dramatic irony is used in many literary works as well as movies and, of course, cartoons. 

There are actually three types of irony: dramatic, situational, and verbal.

Dramatic irony is when the reader or the audience knows something that the characters don't know. For example, the audience might know that someone is waiting around a corner with a knife when a character walks in, but that character doesn't know that he's about to be attacked.

Situational irony is when something unexpected happens after full efforts to avoid or create the situation occur.  For example, if a bride purposely plans to have her reception indoors because there is a chance of rain on her wedding day, but then the sprinkler system in the reception center goes off and everyone gets wet anyway, that's situational irony.

Verbal irony can sometimes be taken as sarcastic, but it is when a name or adescriptong of someone or something shows the opposite of what is real. For example, a boyfriend calls his girlfriend "Tubby" when she is really skinny.

Dramatic irony is established when the audience knows information that a character in a play, story, etc. does not.  For example, in Romeo and Juliet, the audience knows that Juliet is not dead when Romeo comes to her tomb, but he does not and kills himself, thus creating irony.  Another example can be found in Othello. The audience knows from the beginning that Iago is plotting against Othello, but he remains unaware of Iago's treachery until the end of play when he realizes that he killed his wife based on false accusations created by Iago.

What is irony, specifically dramatic irony?

To understand dramatic irony, it is important to understand the meaning of irony and the three basic types of irony.

Irony basically means “To say one thing but to mean something else.” 

Irony defined is a dryly humorous figure of speech in which the literal meaning of a word or statement is the opposite of that intended. In literature, it is the technique of indicating an intention or attitude opposed to what is actually stated.

Many stories will have one or more of these types of irony: verbal; situation; and/or dramatic.

Verbal irony---This type of irony has comes when words have a duality of meaning.  This is the classic form of irony.  The words that are used carry a double message.  The first meaning of the word runs parallel to the mocking or sardonic meaning ascribed to the word. Irony is neither bitter nor sarcastic.  The character in the story primarily uses his ironic words as controlled exaggeration. 

Situational irony—This type of irony is found when actions have an effect that is the opposite from what was intended or expected. Situational irony is also called irony of events. This irony is best defined as a situation where the outcome is inconsistent with what was anticipated. An example might be if a man takes great care to avoid stepping in dog poop and instead slips and falls in it because of a banana peel.

Dramatic irony—This type of irony is used when the audience has knowledge of the fate awaiting the characters. "The characters expect their actions to lead them to triumph, but since readers know what lies in store, the characters’ confidence is ironic."  Dramatic irony makes the characters have an inescapable fate, which replaces suspense with tension as readers know that outcome.

In addition, dramatic irony occurs when "the words and actions of the characters have a different meaning for the audience or reader than they have for the characters." The reader knows more than the characters do.

Examples of dramatic irony

“The Cask of Amontillado” is a perfect example of dramatic irony.  Montresor, a murderer, relates the details of the murder of his enemy fifty years after the crime.  Fortunato, his rival, insults Montresor.  The reader knows from the beginning what is in store for the ironically named Fortunato, who fate is not lucky.  Montresor lures Fortunato down into a catacomb by referring to Fortunato’s weakness, wine.  Montresor claims that he knows that Fortunato is an expert concerning Amontillado, a rare wine. Fortunato expects to drink some wine. Because he has already had too much to drink, he misses very clue that Montresor drops along the way.  The story culminates in the shackling of Fortunate in a niche and being entombed while alive.

Another example comes from Shakespeare’s  Julius Caesar.  In Act II, Julius Caesar’s wife Calpurnia has a bad dream which frightens her.  She tells Caesar that he should not go to the Capitol despite the fact that he is to be offered the crown of Rome that day.  After hearing from the prophets who have opened an animal and discovered it had not heart, Caesar decides that he will stay at home.  The audience knows that the conspirators plan to assassinate him that day.  When all of the conspirators show up to escort Caesar to the senate, Caesar is proud that his good friends have come to take him to the Capitol.  He changes his mind and goes with them. The audience knows that he goes to his death. This is dramatic irony.