Hamlet Act IV, scene 7, lines 118 - 123. Why are these lines important in this play?
I hope that my line numbering matches the text you are referring to. This scene, in total, is the conversation in which Laertes and Claudius plot to kill Hamlet in vengeance for Hamlet's killing Polonius. In this entire scene, Claudius is a master manipulator. He quickly disways Laertes from killing him, and quickly redirects Laertes's anger towards Hamlet. He manipulates Laertes into thinking that Hamlet is jealous of his fencing abilities, suggesting that Laertes has quite a reputation for his skills and that Hamlet would like the challenge of fencing him. Finally, Claudius delivers the lines you are asking about: he is really pushing all of the guilt buttons on Laertes when he asks him, "was your father dear to you? / Or are you like the painting of a sorrow, / a face without a heart?" Clearly he knows that Laertes is devastated over the loss of his father, but he doesn't want Laertes to lose his drive or his focus. I painting of sorrow is flat and lifeless, incapable of action. He wants to make sure that Laertes doesn't "lose the name of action" when he actually get to confront his father's killer. He knows, like Hamlet says earlier in the "To be or not to be" soliloquy that action is sometimes abated or delayed by any number of distractions and thoughts. He doesn't want that to happen to Laertes.