How many ages hence
Shall this our lofty scene be acted over,
In states unborn and accents yet unknown!
Cassius speaks these words in Act 3, Scene 1 just as he convinces the exultant conspirators to smear their hands with Caesar's blood. At this moment of highest drama, one of the chief actors of this piece draws attention to its theatricality. Why?
It is a common trope of Elizabethan thinking to draw attention to life's fictions. Queen Elizabeth staged many public processions and scenes and created and lived the role of the Virgin Queen. Her subjects were both her fellow actors and her audience. Playwrights of the time, and Shakespeare in particular, made use of this metaphor in a number of ways (for an interesting example, take a look at Hamlet and the play within a play, The Mousetrap).
In Julius Caesar, theatricality is both an example of one of the major themes of the play, persuasion, and a comment on the deterioration of the state of Rome. A number of characters use theater in an attempt to persuade.
During the first meeting of Cassius and Brutus, (Act I, Scene 2), they hear a number of shouts. Later in the scene, Casca enters and reports on the offstage theater that has taken place. Caesar has staged a mock refusal of the crown, thinking that he will build a desire in his audience (the plebeians) that he eventually accept it. Think of this as someone refusing an award, saying, "Oh no, I couldn't possibly . . . oh no . . . well, if you insist." (For another example of this dramatic effect, one which works more successfully for the protagonist, see Shakespeare's Richard III.) Caesar's stage managing backfires though, and instead of acclaiming him, the people behave like a real audience passing judgement on the quality of the spectacle. "If the tag-rag people did not clap him and hiss him / according as he pleased and displeased them, as they use to / do the players in the theatre." Caesar's performance isn't good enough. It proves his superficiality. The people perceive this and refuse to accept him as their ruler.
Antony is much more successful with his theatrics. Unfortunately, Brutus does not recognize what Antony is up to when he asks to give Caesar's funeral oration in Act III, Scene 2. The opportunity to stage a scene is evident to the reader and to at least one of the conspirators, Cassius, who tries to dissuade Brutus, but to no avail. Imagine the power of Antony's entrance as he bears Caesar's body in his arms. This is a exhibition meant to move an audience — and it works. Antony's persuasive rhetoric that follows allows him to realize his objective: to incite the mob to revolt against the conspirators, with another showy scene. When Antony gradually uncovers Caesar's body and exposes its wounds, the first Plebeian responds with "O piteous spectacle" and that is precisely what it is. By means of the theatrical, then, the people have been convinced to act, not in their own best interests but in the interests of Antony, Octavius, and Lepidus. Theater's power has been to continue the strife rather than to resolve it. To an Elizabethan audience, such dramatic tension would have been both threatening and seductive.