In the context of Industry 5.0, where human-centred collaboration is paramount, effective interaction between humans and Cyber–Physical Systems (CPS) requires us to reconsider the traditional concept of interoperability. Although technical, syntactic and semantic interoperability facilitated system integration in Industry 4.0, they are insufficient when humans become active collaborators. In particular, semantic interoperability fails to capture the cognitive and contextual nuances of human reasoning, often resulting in gaps in mutual understanding. This article discusses and defines cognitive interoperability, which goes beyond semantic alignment by integrating shared perception, contextual modelling, and reasoning mechanisms to support seamless collaboration between humans and CPS. First, we provide a comprehensive analysis of how cognitive interoperability has been defined in various fields, offering a unified and clarified perspective. Next, we present a structured diagram detailing the cognitive functions necessary to achieve cognitive interoperability between humans and CPSs. Finally, we examine a real-world use case in the field of Human–Robot Collaboration (HRC) to illustrate the practical implications of this concept. Through this example, we demonstrate how cognitive interoperability can address the limitations of semantic interoperability in dynamic and cooperative contexts by enabling mutual understanding and adaptive interaction. Our work contributes to advancing human-centred intelligent systems and provides a foundation for designing next-generation collaborative manufacturing environments.