As computational systems supported by artificial intelligence (AI) techniques continue to play an increasingly pivotal role in making high-stakes recommendations and decisions across various domains, the demand for explainable AI (XAI) has grown significantly, extending its impact into cognitive learning research. Providing explanations for novel concepts is recognised as a fundamental aid in the learning process, particularly when addressing challenges stemming from knowledge deficiencies and skill application. Addressing these difficulties involves timely explanations and guidance throughout the learning process, prompting the interest of AI experts in developing explainer models. In this paper, we introduce an intelligent system (CL-XAI) for Cognitive Learning which is supported by XAI, focusing on two key research objectives: exploring how human learners comprehend the internal mechanisms of AI models using XAI tools and evaluating the effectiveness of such tools through human feedback. The use of CL-XAI is illustrated with a game-inspired virtual use case where learners tackle combinatorial problems to enhance problem-solving skills and deepen their understanding of complex concepts, highlighting the potential for transformative advances in cognitive learning and co-learning.