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The integration of artificial intelligence (AI) and machine learning (ML) into materials science has revolutionized the discovery, design, and optimization of new materials, enabling accelerated predictions of properties and behaviors previously unattainable with traditional methods. However, the “black-box” nature of many advanced AI models poses significant challenges, including a lack of transparency that hinders scientific understanding, trust, and practical adoption in materials research. This narrative review explores the concept of interpretability in materials AI, focusing on what constitutes an “explanation” and how it should be conceptually evaluated. Drawing from recent advancements in explainable AI (XAI), we delineate definitions of explanations tailored to materials informatics, emphasizing their role in bridging computational predictions with physical insights. We examine thematic aspects such as intrinsic versus post-hoc interpretability methods, the multidimensional nature of explanations (e.g., local vs. global, feature-based vs. mechanistic), and conceptual frameworks for evaluation, including criteria like fidelity, comprehensibility, robustness, and domain-specific relevance. By synthesizing the literature, we highlight how explanations can enhance materials discovery across alloy design, catalyst development, and polymer engineering, while addressing gaps in current evaluation practices. The review underscores the need for standardized conceptual metrics that go beyond quantitative benchmarks to incorporate qualitative, human-centered assessments in materials science contexts. Ultimately, this work aims to guide researchers toward developing interpretable AI systems that not only predict but also elucidate underlying material phenomena, fostering a more insightful and ethical application of AI in materials innovation.