Banquo's ghost appears in act 3, scene 4, and sits down in Macbeth's place. The fact that Banquo's ghost chooses to sit in the king's seat is significant because it foreshadows how Banquo's descendants will inherit the throne, as the witches predicted. The fact that Macbeth hallucinates and sees the ghost also reveals the king's current mental state. Macbeth is clearly overwhelmed with guilt and beginning to lose his mind. Macbeth's guilt and unsteady mental state foreshadow his malevolent reign as a bloodthirsty tyrant.

This particular scene is also significant in regards to how the other Scottish nobles view Macbeth. Initially, they support Macbeth's kingship and believe that Malcolm and Donalbain are responsible for their father's death. However, Macbeth's inability to keep his composure combined with his strange behavior signify that all is not well in the kingdom, and the nobles begin to question Macbeth's involvement in Duncan's death.

There are definitely two reasons for the appearance of Banquo's ghost at the banquet. First, he is a reminder of Macbeth's guilt and foreshadows even more deaths to come as well as Banquo's lineage and claim to the throne. Second, since the guests see Macbeth's reaction, they can interpret it for themselves. They realize that something is rotten in the state of Scotland and can conclude that Macbeth is guilty of murder, perhaps more than once. Ultimately, Banquo's ghost confirms Macbeth's sins, both to himself and to his peers.

An interesting question. Banquo's ghost is important for at least three reasons.

First, ghosts appear when someone is dead (obvious, right), and, especially, when someone died with something left undone or been killed in an evil manner. This ghost is an accusation.

Second, it seems like only Macbeth can see this ghost. This isolates him. Is he going mad? Living in a private reality?

Third, when the ghost enters, it takes Macbeth's place at the table. We can take this as a sign—a kind of omen. There's a dead guy in your place; you will be dying soon.