Final answer:
Claudius is referring to the biblical curse of Cain and Abel, acknowledging that his act of murdering his brother carries a grave, divine punishment.
Step-by-step explanation:
When Claudius refers to "my offense is rank, it smells to high heaven; It hath the primal eldest curse upon't, A brother's murder", he is alluding to the curse of Cain and Abel from the Bible. In the Book of Genesis, Cain commits the first murder by killing his brother Abel, and as a result, is cursed by God. Claudius invokes this curse, recognizing that in murdering his own brother, King Hamlet, he has committed a similarly grave sin and is now subject to divine punishment.