What is dramatic irony?

Dramatic irony is when you, the reader of the novel or spectator of the play, knows something that the characters do not. It is a literary technique mostly used in plays, and can take various forms. 
Examples:
1) You are watching a play and you see a character poisoning a drink. When another character goes to drink it, you know what will happen before they do.
In this instance the technique is used to heighten the drama of a play, or provide pity for a character
2) Some playwrights are more historical, for example in ‘An Inspector Calls’, Mr Birling talks about the unsinkable Titanic. However everyone watching the play knows that the Titanic will sink. 
Here the technique is used to show how naïve characters can be, and how people have false beliefs
3) It can also be used in films! For example in Snow White we all know that the apple the old woman gives to Snow White is poisoned before she does.
Not only is dramatic irony present in modern films and literature, but it goes back to the beginning of the English language playwriting tradition. One author who uses the technique a lot is Shakespeare:
1) In Macbeth, we know that Macbeth and Lady Macbeth are going to betray Duncan before he does. We know that they invite him to the castle for the sole purpose of killing him so that Macbeth can become King, but he thinks it is a genuine act of kindness. 
The effect here is to create suspense - we know that Duncan will be killed but we don’t know when. The audience watching the play wonders when Duncan will really find out his fate.
2) In Romeo and Juliet, the audience knows that Romeo has faked his death so he can be with Juliet.
Juliet doesn’t know this so proceeds to kill herself - this wouldn’t have happened if she had known everything the audience had!
The purpose here is to create pity and grief in the audience - we pity Juliet because she did not have to die, and if she had waited she could have been with the man she loved.
Dramatic irony is always present in literature so watch out for it! Lots of things can count as dramatic irony, so always think about whether you know something before a character does. If so, it must be dramatic irony.