Polonius wants Reynaldo to go to France and visit Laertes while spying on him to see what he's up to and make sure that he is behaving properly and keeping up the reputation and image of the King of Denmark. He is to do this by asking around implicitly about Laertes and saying that he knows him faintly and making up little lies to see if people who know him or have seen him agree with him and eventually tell of what they've seen Laertes do, essentially through roundabout means.
