Act 3, Sc. 2, Lines 1-25: What does Hamlet mean by the following words, and why does he want to emphasize that for this play?

Hamlet's intent is to have the players recreate the death of his father.... he wants the acting to mirror Claudius' part in Old Hamlet's death. He wants Claudius to understand the meaning behind the scene in question. In this way, Hamlet believes he can ascertain for certain that Claudius is guilty.