In Act 4, why does Caesar's ghost appear?I don't understand why Caesar's ghost shows up. I dont understand the significance of that scene.

In Shakespeare's Julius Caesar, the
Ghost is a bad omen for Brutus.  Brutus betrayed Caesar by taking part in the conspiracy
against him and helping to assassinate him.  In a play that involves numerous omens (see
Act I.3, for instance), this one has a specific target.  Whereas other omens reflect the
unnatural state of political upheaval in Rome, this omen directly suggests that Brutus
is about to take a fall, and Caesar is about to be
avenged.

If the deceased Caesar is at Philippi in the form
of the Ghost, as the Ghost says he will be, that suggests the battle that will take
place there will not go well for Brutus.  Brutus is about to "get his" for what he did
to Caesar. 

The Ghost, then, serves as foreshadowing of
what's to come by presenting an omen that reveals that the plot is about to come full
circle.  Brutus will fall because of his poor decision-making and his poor judgment of
others, such as Cassius.  He will fall because of his part in Caesar's
assassination.

The Ghost sets the mood for the remainder of
the play.  Brutus is doomed.  He and Cassius both know it, or at least suspect it.  The
appearance of the supernatural gives an air of fate or destiny to what
follows.