Why does the ghost reappear in Act 3, Scene 4?
The reappearance of the ghost has symbolic significance beyond simply spurring Hamlet on to revenge or clearing Gertrude of any wrongdoing. It seems that Shakespeare wishes to associate the depth of his characters’ sensibilities and levels of awareness to their relative sensory experiences of the ghost. For example, the sentries are able to see the ghost but neither hear him nor speak to him. They, as a whole, are aware that something is rotten in the state of Denmark, although they cannot quite deduce the cause of the disintegration. Hamlet, on the other hand, is not only able to see the ghost but he is also able to hear the ghost’s words and speak to him. Hamlet is, of course, fully aware of how rotten the State of Denmark is, as well as of the cause of its disease. The reappearance of the ghost in Act 3, Scene 4, therefore, guides the audience to a more favorable interpretation of the naive Gertrude. Shakespeare intends the audience to regard her as a wholly innocent victim, oblivious to the gambits of her current husband and unaware of the depths of both Hamlet’s psyche and mandate. This interpretation allows the audience to regard Claudius as the true antagonist of the play instead of mistakenly believing Gertrude might serve in this capacity, a grave misinterpretation committed by even some renowned scholars such as T. S. Eliot.
The ghost also hints here that Gertrude might have been involved in the plot to take King Hamlet's life. However, he instructs Hamlet not to take revenge on his mother, but to concentrate on Claudius, who actually poured the poison in King Hamlet's ear as he slept and took over his life.
The ghost reappears to instruct Hamlet to comfort his mother. She is overwrought at her son's behavior and words. Hamlet believed that the ghost was there to tell him that his father was angry at him for not taking his revenge.