Falnavar's state is deteriorating and his last wish is that you take the vengeance that he can no longer claim.
'Go...
'Find that cur, Yarikh and put a final end to the misery he has caused. See him pay for the--'
He coughs madly, winces, and regains himself.
'Make him pay for the pain he wrought upon my brethren... my crews... my people.
'Fulfil this wish; the final wish of a dying man.'
The last request? Perhaps. Speak with the mariner to go to the place where Yarikh is, and defeat the Corsair villain, once and for all.
Return to the mariner and speak with him to inform him that the deed is complete.
Falnavar's death is tragic, but there is a final note that he provided you.