In "Julius Caesar," the role of Caesar's ghost is similar to that of ghosts in "Hamlet" and "Macbeth"; that is, the apparition stirs the conscience of the character who sees it and portends further evil.
In Act IV, Caesar's ghost appears to Brutus, who is between consciousness and sleep as he reads in his tent before the battle at Philippi. When he sees the ghost, Brutus asks, "Speak to me what thou art," and the ghost replies, "Thy evil spirit, Brutus" (IV,iii,280-281). This statement by Caesar's ghost stirs the conscience of Brutus for his past acts as well as disturbing him as he ponders his future battle.
So, Brutus, who has made errors in judgment earlier such as allowing Marc Antony to live after the assassination, begins to have pangs of conscience over his guilt for another poor judgment: killing his friend, Caesar. He also may be experiencing a premonition as the ghost tells him, "To tell thee thou shalt see me at Philippi"(IV,iii, 282).
The spirit of Caesar is present each time Brutus makes a poor decision as well as each time he has a pang of conscience for an evil act. For, Brutus's initial act against Caesar, his murder, while committed for principle by Brutus, was done for cupidity by others. Secondly, shortly before Caesar's appearance, Brutus, in tragic arrogance, argues almost to the point of murder again as he and Cassius discuss Brutus's failure to aid Lucius Pella, a friend of Cassius. Thirdly, with the next appearance of the ghost, the battle of Philippi, Brutus commits a fatal error in military judgment as he rushes onto the field, but must later retreat. This defeat leads to the suicide of Brutus.