The character who turns away to the audience is saying something that should not and cannot be heard by his counterpart. That is to say, the ontological borders of the world on stage are broken and a new one is created in the direct address of character to audience. In terms of theatricality this may concern many sorts of situations in real life. In the case of a court, for instance, as was also indicated by Quintillian, there will be different addressees with different roles. There is a judge or a jury, there is someone accused and perhaps an accuser; there may be a general audience watching, or an audience that consists of relatives and friends. In speaking to the accuser first, for instance, a lawyer may turn away to the judge. Or in speaking to the jury she may turn away in order to start to speak to the audience. The shift in audience implies a shift in mode. One shifts from interrogation, for instance, to explanation. So, even when, in the context of a court, the addressee from which one turns away will still be able to hear the text that is addressed to another person, his status will have changed because the address shifts modes. In this lies the “wonderfully stirring” rhetorical power of apostrophe. 
Note 5: Longinus, in his study on the sublime also emphasizes how the change of person has a “vivid effect” (Longinus 1995: 200, 201).