In short, Brutus's defeat and death is foreshadowed by the appearance of the ghost, which tells Brutus that "thou shalt see me at Philippi." Many theatergoers in Shakespeare's time would have known that Brutus was doomed to die for his role in the assassination of Caesar, and that his death would have occurred at Philippi (which Brutus has already mentioned as the place where their army is going). So when Caesar's ghost, which describes itself as "thy evil spirit," tells Brutus that it will visit him again at Philippi, it is fairly clear that he is predicting his death. However, much like in Macbeth, the appearance of a ghost is used by Shakespeare to suggest that Brutus is experiencing pangs of regret and remorse for murdering Caesar. The ghost is a manifestation of his guilt, and of his growing sense that his evil deeds will revisit him. The fact that none of his sleeping lieutenants see the ghost and that the ghost calls itself Brutus's own "evil spirit" reinforces the idea that it is perhaps a figment of Brutus's own conscience and his sense that things are not, to say the least, going to end well for him.
Caesar's ghost is a manifestation of Brutus' guilty conscience. Only Brutus sees it, so it is possible that the ghost only exists in Brutus' mind. It is at Philippi where Brutus becomes reiterates that he would give his life for his country, and seeing how he was part of the civil war that broke out in Rome, Brutus believes he deserves to die. He had honestly believed that assassinating Caesar was in Rome's best interest. However, after misjudging Marc Antony by thinking that he was not a threat and then becoming partners with someone like Cassius who has been reported to have accepted bribes, Brutus realizes his role in the destuction of what he loved more than friends (like Caesar) and family (like Portia)...Rome. The appearance of Caesar's ghost forshadows the realization in Brutus as well as his suicide.