What is the significance of this quote?Laertes, was your father dear to you?Or are you like the painting of sorrow,A face without a heart? (Act IV,...

In Shakespeare's Hamlet, the significance of the quote you mention is that Claudius is in the process of manipulating Laertes into killing Hamlet for him.  He's tricking Laertes into doing his own dirty work, so to speak.  And Laertes is gullible enough and rash enough to fall for it. 

Claudius is daring Laertes to be man enough to avenge his father's death at the hands of Hamlet.  He uses a warped sense of logic to step-by-step lead Laertes to do what he wants him to do. 

First, in the quote you mention, Claudius questions how much Laertes loves his father.  Then he talks about how time can weaken love and weaken what love can make us do.  Claudius worries that time will weaken Laertes' love, he infers. 

What Claudius is really after is then revealed:

Hamlet comes back; what would you undertake

To show yourself in deed your father's son

More than in words?  (Act 4.7.122-124)

Claudius wants action from Laertes, not just words.  And the action he wants is for Laertes to kill Hamlet. 

In the next few lines Claudius outlines his plan to create a match between Laertes and Hamlet, during which Laertes will use a sword "unbated" and will kill Hamlet "for your [Laertes'] father."

The lines you quote are the first step of manipulation Claudius uses to get Laertes to kill Hamlet for him.  And Laertes not only falls for it, but contributes to the plan himself, suggesting he will poison the unbated sword tip, just to make sure.