The Real refers to the real world within the Amory Wars. It is the opposite of the Fiction written by the Writer, which is the fictional universe in which Heaven's Fence exists.
Good Apollo I'm Burning Star IV Vol. 1 - From Fear Through the Eyes of Madness Edit
The Real is only visited during Good Apollo 1, when the story shifts from the perspective of Claudio to the perspective of the Writing Writer. In it, he is suffering from his own personal demons stemming from the departure of his longtime girlfriend and lover Erica Court, and is constantly shifting between the Fiction and the Real as his madness intensifies.
Meanwhile, those in the Fiction are unaware of the Real or the Writer until an incident involving the Willing Well, a mirror that acts as the Writer's gateway between the Fiction and the Real, in which the Writer and Claudio Kilgannon confront each other. The Writer, God in the Fiction, reveals he intends to kill Ambellina to mend his broken mind and end his suffering. Claudio stands ready to defend Ambellina, but even the godly powers of the Crowing are nothing against a real entity, and Ambellina is murdered by the Writer. He then departs, leaving Claudio in despair.