Why does Claudius send Cornelius and Voltimand to Norway? (lines 27-39)
These two men are found in Act I, Scene 2.
The reason that Claudius is sending them to Norway is to ask the King of Norway for his help. The King of Norway has a nephew named Fortinbras. Fortinbras is angry at Denmark because the old king Hamlet killed Fortinbras's father, who was king of Norway. In order to get revenge, Fortinbras is gathering troops and planning to attack Denmark.
Claudius is sending the two men to tell the King of Norway to get with it and prevent Fortinbras from attacking Denmark. Here is the relevant passage:
To Norway, uncle of young Fortinbras,
Who, impotent and bedrid, scarcely hears
Of this his nephew's purpose, to suppress
His further gait herein, in that the levies,
The lists, and full proportions are all made
Out of his subject; and we here dispatch
You, good Cornelius, and you, Voltemand,
For bearers of this greeting to old Norway,
Claudius, the usurper of Denmark's throne, is quite the politician. He understands that the current King of Norway is weak and sickly and that his young nephew, Fortinbras, plans to strike against Denmark for the restoration of lands lost to Hamlet's father. Claudius hopes that by sending an appeal with his courtiers Cornelius and Voltemond, that the king of Norway will rein in his nephew and avert the attack on Denmark. Some might consider his action weak, but it does prevent young Fortinbras from invading Denmark.
Cornelius and Voltemand are minor characters who simply do Claudius's bidding, not unlike Rosencrantz and Guildenstern later in the play. Claudius does not want them to be seen as powerful, and he makes it clear to them that he is only granting them limited power:
"Giving to you no further personal power
To business with the king, more than the scope
Of these delated articles allow."