What is dramatic irony, specifically in Romeo and Juliet?
Dramatic irony is when the reader knows more than the characters in the book.
Since we're talking about Romeo and Juliet, look at the preface of Romeo and Juliet. In that sonnet, Shakespeare tells us that Romeo and Juliet will die in the end. With that information, the readers now know more information than the characters: Romeo and Juliet.
If Romeo and Juliet knew their future, they would have, more than likely, done something more to prevent them from dying. But, since they didn't, they end up killing themselves, foreshadowed by Shakespeare.