Rhetoric is the art or science that aims to study the capacities needed to inform, persuade, or motivate particular audiences (rhetorician). Furthermore, it is the art or science that seeks to achieve clarity, awaken our sense of beauty, or bring about mutual understanding (rhetor). (James A Herrick).
This is the first time in the article that mentions the definition of Rhetoric. If I were to paraphrase, Rhetoric is the structured process of bridging your ideas across to another group in the hopes of persuading that other group with your ideas.