Who's Heath Ledger? And what's Florida like?
Here's an extract from The Vampire Diaries. Bonnie thinks she's a psychic. She has already predicted Heath Ledger and believes that Florida will broke off.
[MISSING PERSONS: BROOKE AND DARREN BEHIND ELENA ON TV]

Scene Change:BONNIE'S CAR

[Elena and Bonnie are driving to school in Bonnie's car.]

BONNIE: So Grams is telling me I'm psychic. Our ancestors were from Salem, witches and all that, I know, crazy, but she's going on and on about it, and I'm like, put this woman in a home already! But then I started thinking, I predicted Obama and I predicted Heath Ledger, and I still think Florida will break off and turn into little resort islands. . .Elena! Back in the car.

ELENA: I did it again, didn't I? I--I'm sorry, Bonnie. You were telling me that. . .

BONNIE: That I'm psychic now.

ELENA: Right. Ok, then predict something. About me.

BONNIE: I see. . .

Question

Who's Heath Ledger? And what's Florida like?
Here's an extract from The Vampire Diaries. Bonnie thinks she's a psychic. She has already predicted Heath Ledger and believes that Florida will broke off. 
[MISSING PERSONS: BROOKE AND DARREN BEHIND ELENA ON TV]

Scene Change:BONNIE'S CAR

[Elena and Bonnie are driving to school in Bonnie's car.]

BONNIE: So Grams is telling me I'm psychic. Our ancestors were from Salem, witches and all that, I know, crazy, but she's going on and on about it, and I'm like, put this woman in a home already! But then I started thinking, I predicted Obama and I predicted Heath Ledger, and I still think Florida will break off and turn into little resort islands. . .Elena! Back in the car.

ELENA: I did it again, didn't I? I--I'm sorry, Bonnie. You were telling me that. . .

BONNIE: That I'm psychic now.

ELENA: Right. Ok, then predict something. About me.

BONNIE: I see. . .

Answer

Heath Ledger was an Australian actor who died in 2008 from overuse of prescription medication. Apparently a psychic really had predicted his death, so they put the reference in the show.

The state of Florida is a strip of land in the Southeast part of the United States. Because if its shape and position, it could eventually break off from the rest of the country - maybe in a million years or so.

Answer

Heath Ledger was a semi-famous actor before his death at a young age.  It seems like Bonnie was able to predict that he would die.   Bonnie also believes that the American state of Florida is going to separate (break off) from the rest of the continental United States and become a number of little islands (in the Atlantic Ocean and Caribbean Sea.)

Answer

Heath Ledger's death has kind of been a popular topic in American pop culture, because of his strange behavior before his death relating to a role he had in a film. Many people believe that because he was playing a mentally deranged character in a film he was working on, he became mentally deranged himself. The film was the second of the newer Batman movies, and he played the Joker, if you are interested to see it.

Florida is warm and humid. It is flat and has some marshland and beaches. Many retired Americans will go to live in condos there because of the warm weather. I personally don't think it is very nice there.

Answer

Heath Ledger was a young actor who killed himself. Florida breaking off may refer to an earthquake or political secession, I'm not clear.