Eh, I wonder if it's just a different interpretation, but it seems pretty obvious to me. Hamlet's talking about death, and what comes after death, and how nobody know because it's "the undiscovered country" that no one returns from, so he's afraid of what might happen to him after death if he kills himself.

Considering all the Shakespeare references in TOS that they didn't screw up, I'm surprised by this one. *shrugs*