What is Laertes' filial duty in "Hamlet"?
Filial duty just means the duty a son owes to a father. And, as Hamlet's duty is to revenge his father's murder, and as Fortinbras (in the final act) invades Denmark in order to revenge his father, Laertes returns to Elsinore to revenge the death of his father, Polonius.
The scene to look at is Act 4, Scene 5, in which Laertes openly states that he will perform his filial duty even if it means that he goes to hell:
I dare damnation. To this point I stand,
That both the worlds, I give to negligence,
Let come what comes; only I'll be revenged
Most throughly for my father.
With Claudius, Laertes then concocts a plan to kill Hamlet, who killed Polonius (behind the arras, thinking he was killing Claudius) in the closet scene.