In "Hamlet" what reason did the Ghost give Hamlet for its second appearance?
The ghost states that he is there "to whet thy almost blunted purpose" (III.iv.111), meaning, to remind Hamlet of what he asked him to do in the first visit: enact revenge on Claudius for killing him. Hamlet was afraid of that, because the first thing he says when he sees the ghost is "do you not come your tardy son to chide, that...lets go by the important acting of your dread command?" (III.iv.105-7). Hamlet knows that he is "tardy" in enacting revenge as his father's ghost commands. He has been busy trying to determine if Claudius did indeed kill him, because he doesn't want to murder someone based on a ghostly image's accusation.
But even a reminder of the ghost's commission is yet not enough to prompt Hamlet to immediate action; it takes the discovery of Claudius' note to Rosencrantz and Guildenstern to finally act, manipulating their murder and returning home ready to rumble.
The Ghost of Hamlet's father appears to Hamlet for the second time in Act III sc.4. in what is known as the 'closet scene.' Hamlet has just then accidentally killed Polonius who was hiding behind the curtains in the room and he begins to scold his mother vehemently for marrying Claudius, "a murderer and a villain." Poor Gertrude is greatly distressed and is unable to bear his accusations and cries out, "no more," but Hamlet doesn't relent and continues accusing her. It is at this moment that the Ghost appears to Hamlet for the second time and tells him,
"Do not forget: this visitation
Is but to whet thy almost blunted purpose."
The Ghost reminds Hamlet that his main aim and purpose should be to take revenge on Claudius by killing him instead of wasting his time and energy by merely accusing his mother and quarrelling with her. The Ghost feels that Hamlet has delayed taking revenge on Claudius for such a long time and so he has visited him for the second time ("to whet" meaning 'to sharpen,' 'to make keener') to rekindle and intensify his desire to kill Claudius.
The Ghost departs after it sees Hamlet comforting and consoling his mother in obedience to its wishes.