The play does not explain the title. What the text shows is that Caesar, after dying in Act III, scene 1, remains present in three ways: as a body, as a ghost, and as a name. That the title is explained by this is an interpretation, but each of the three modes can be checked in the text.
Alive, Caesar appears in few scenes and speaks of himself by his own name. In Act I, scene 2, he tells Antony that he fears nothing and only points out what should be feared, because "I shall always be Caesar." On the morning of the Ides (Act II, scene 2), he says that Caesar will go out, answering Calpurnia's fear.
Dead, he does not leave the play. In the Forum (Act III, scene 2), Antony shows the people the body and the torn cloak. In Act IV, scene 3, the ghost appears to Brutus, says it is his evil spirit, and promises to meet him at Philippi. In Act V, scene 3, before the bodies of Cassius and Titinius, Brutus cries out that Caesar's spirit is still mighty, and the sword with which Cassius died, a little earlier in the same scene, is the one that pierced Caesar.
The name also passes on. The list of characters calls Octavius "Octavius Caesar," Antony addresses him as Caesar at Philippi (Act V, scene 1), and Brutus answers him in the same way. Dying, Brutus tells Caesar's spirit that it may now rest.