This line is spoken in Act IV, Scene 1. It is spoken by King Claudius to Queen Gertrude. He is talking about what must be done with Hamlet now that Hamlet has killed Polonius.
To understand the significance, you have to know what it is that Claudius is talking about here. He is talking about "slander." He is saying that slander (I think he simply means any words that will make him look bad) can go all the way around the world and still hit its target. He is hoping that it will miss him and hit only air.
So he is very worried about what people are going to say about him given what Hamlet has done. He hopes that by sending Hamlet away and by telling all the important people that Hamlet killed Polonius, he will make people think badly of Hamlet and not think badly of him (Claudius).
Get Ahead with eNotes
Start your 48-hour free trial to access everything you need to rise to the top of the class. Enjoy expert answers and study guides ad-free and take your learning to the next level.
Already a member? Log in here.