Guided by the principles of three-way decision theory, emphasizing thinking, problem-solving, and computing in threes, we examine several triadic structures that provide insights for eXplainable Artificial Intelligence (XAI). In this paper, we propose a framework to explain XAI at three levels. At the top level, we conceptualize XAI through the Social-Machine-Human triad, addressing three foundational concerns regarding, the social considerations of what AI should or should not do, the machine capabilities of AI systems of what machines can do, and the human-centric concerns of what human can easily understand and trust. At the middle level, we highlight the machine aspect of XAI by adopting the input-process-output (IPO) triad to describe the functioning of an AI system. At the bottom level, we introduce three specialized triads to further explain the IPO triad. The volume-veracity-validity triad refines the input component, the theory-algorithm-implementation triad clarifies the process within computation, and the symbol-meaning-value triad describes the output. This trilevel framework aims to provide a holistic, structured foundation of explaining XAI as a field of research.