Cornelius and Voltemand are Danish ambassadors who are sent in Act 1 scene 2 on a diplomatic mission to the King of Norway. The King of Norway is an old man, and it seems he is not in full control of the country; in particular his nephew Fortinbras is insisting that Denmark return to Norway some lands the Fortinbras argues are rightfully theirs. Voltemand and Cornelius are charged with going to the King of Norway to try to corral Fortinbras diplomatically; though we have already learned in the first scene that Denmark has ramped up munitions production in case the matter needs to be settled on the battlefield. The diplomats return having, it seems, succeeded, but later we learn that Fortinbras will not be deterred.
Cornelius and Voltimand are ambassadors that King Claudius is sending out to Norway. They are being sent to ask the king of Norway to keep his nephew a little more under control. This happens in Act I, Scene 2.
Fortinbras is the nephew of the king of Norway and the son of the former king. His father had been killed by Hamlet's father. Because of this, Fortinbras is making trouble and seems like he might be going to attack Denmark. King Claudius sends Cornelius and Voltemand to try to get the king of Norway to calm Fortinbras down.