Dramatic irony most associates itself with situations in which there is a key feature of a story, often a surprise which will undo the primary character, which the audience or at least another member of the story knows about.
Most commonly a form of dramatic irony called "tragic irony" is employed heavily by Shakespeare. An example of this would be in the final scenes of Romeo and Juliet, in which the audience is aware that Juliet, whom Romeo has just found apparently dead, is in fact drugged and simply appears to have died. In his sorrow, Romeo then kills himself. When Juliet wakes, she finds the tragic Romeo and thus kills herself. Tragic, I'm sure you'll agree!
Dramatic irony is not, of course, simply a secret kept from the protagonist, however, it is in this form that the most poignant examples of this type of irony form and provide a very entertaining method of storytelling.