At the beginning of the scene, Claudius orders Rosencrantz and Guildenstern to accompany Hamlet to England. He explains that it is not safe to "let his madness range" in Denmark, and the two old friends of Hamlet will serve as diplomats there while essentially spying on the prince.
Interestingly, Polonius has already done something similar with his son, Laertes, who is at school in Paris. In act 2, Polonius gives Reynaldo some money and letters to take to Laertes but also orders him to ask around to find out what kind of company the young man is keeping. He even develops a plan to coax the truth out of Laertes's friends by making up stories about some minor transgressions (gambling, for instance).
Of course, Polonius is a devious, conniving man who also repeatedly spies on Hamlet. This ultimately gets him killed, when the prince mistakenly stabs him while he is hiding behind a curtain in the queen's chamber. This leads Claudius to reveal that he has sent letters with Guildenstern and Rosencrantz demanding that the English execute Hamlet. Hamlet has already figured out this plan, saying previously that he does not trust the two men anymore than "adders," and he switches letters with them. In short, both Claudius and Polonius have duplicitous plans for their sons.