ster crossed lovers are basically lovers that are doomed. It originated in Romeo and Juliet:
"when a pair of ster crossed lovers take their life..."
Jack and Rose from "Titanic" is another classic example. They're tragic. However, i dont think it necessarily has to mean that they are going to die; it could just mean their relationship will end up failing too. Depends on how u look at it.
Like the person before me said, couples that are doomed. Also if they can't be together and stick together anyway. Some modern examples:
Michael and Nikita: Heard the term "Sleeping with the enemy?" They're on separate sides but together anyway. Michael eventually double-crosses his side, though.
Spencer and Toby: Their parents disapprove of who they're with and basically made it one of those forbidden love stories. They've both been accused of murdering the same person so being together doesn't help them at all, but they're still together, and my OTP.
Katniss and Peeta: Must I explain? They have to kill each other!