The evidence in the play suggests that the ghost of Banquo is Macbeth's hallucination. Consider the events leading up to the appearance of the ghost. Macbeth marks Banquo and his son for death, viewing them as threats to his crown. He is in the midst of a celebration with his family and members of his court when the ghost appears.
Banquo should be there as a guest, he was one of Macbeth's closest friends. Macbeth pretends to wish that Banquo was at the celebration, his false sense of sadness at the absence of his friend may be the cause for the ghost's arrival in the room shortly thereafter.
Macb. Here had we now our country's
Were the grac'd person of our Banquo present;
Who may I rather challenge for unkindness
Than pity for mischance!" (Act III Scene IV)
Macbeth first sees the ghost sitting in a chair and is shocked and frightened by the sight. He can't believe his eyes, but no one else can see the ghost.
" Macb. Prithee, see there! behold! look! lo!
how say you?
Why, what care I? If thou canst nod, speak too.
If charnel-houses and our graves must send
Those that we bury back, our monuments
Shall be the maws of kites." (Act III. Scene IV)
The ghost is persistent, he leaves and then returns.
"Macb. Avaunt! and quit my sight! Let the
earth hide thee!
Thy bones are marrowless, thy blood is cold;
Thou hast no speculation in those eyes
Which thou dost glare with." (Act III, Scene IV)
Lady Macbeth chides her husband for his ravings, she tells him that he is spoiling the party with his wild talk.
"Lady M. You have displac'd the mirth,
broke the good meeting,
With most admir'd disorder" (Act III, Scene IV)
Macbeth continues to question the presence of Banquo's ghost drawing the attention of Ross, who questions him about what he is talking about.
"Macb. Can such things be
And overcome us likes a summer's cloud,
Without our special wonder? You make me
Even to the disposition that I owe,
When now I think you can behold such sights,
And keep the natural! ruby of your cheeks,
When mine are blanch'd with fear.
Ross. What sights, my lord?
Lady M. I pray you, speak not; he grows
worse and worse;
Question enrages him. At once, good-night:
Stand not upon the order of your going,
But go at once." (Act III, Scene IV)
At this point, Lady Macbeth gets very nervous about what her husband is saying in front of his court and she tells everyone to go home that the King is just not feeling well. He is having a kind of fit that will pass.
That's a good question. It certainly doesn't have "reality" in the traditional sense, but like the dagger which Macbeth sees on the way to murdering Duncan, the question is whether Macbeth has entirely imagined it, or whether the witches have something to do with it.
No-one else at the table can see Banquo's ghost. But the audience can. Which gives it a weird status, somewhere between real and unreal. Lady Macbeth says to him:
O proper stuff!
This is the very painting of your fear;
This is the air-drawn dagger which, you said,
Led you to Duncan. O, these flaws and starts,
Impostors to true fear, would well become
A woman's story at a winter's fire,
Authorized by her grandam. Shame itself!
Why do you make such faces? When all's done,
You look but on a stool.
So, yes, it's probably in Macbeth's head - though has it been placed there by the witches, or is it just Macbeth himself, and his sleepless guilt?
Hope it helps!