Here's a breakdown of the key points:
* Hamlet's execution: The letters do indeed contain an order for Hamlet's execution. This is the primary purpose of the mission, as Claudius fears Hamlet's growing influence and potential for rebellion.
* "Private" instructions: The letters also contain some "private" instructions, which are never explicitly revealed in the play. This suggests there's more to the mission than simply killing Hamlet. These private instructions could involve a range of things:
* Spying: Claudius might want Rosencrantz and Guildenstern to report back on Hamlet's activities and any potential allies he might have in England.
* Manipulating Hamlet: The "private" instructions could be aimed at influencing Hamlet's behavior, perhaps by encouraging him to take actions that would further damage his reputation or alienate potential supporters.
* More sinister plots: Claudius's "private" intentions could be far more insidious, such as a plan to frame Hamlet for treason or even manipulate events to have him killed by someone else.
* The "secret" letter: Hamlet, of course, discovers the plot against him and intercepts the letters. He then cleverly replaces one of the letters with a new one, ordering the execution of Rosencrantz and Guildenstern instead. This letter is referred to as "secret" because it's not part of the initial orders, but it's likely written in the same official style as the others, making it appear legitimate.
In summary, the letters sent with Rosencrantz and Guildenstern are more than just a simple death warrant for Hamlet. They represent a complex and dangerous web of plots and schemes, with Claudius manipulating events behind the scenes to ensure his own power and security.