Higher dimensional categories extend the concept of traditional categories in mathematics by incorporating not just objects and morphisms (arrows between objects), but also higher-level relationships between these morphisms. This means that in addition to having objects and arrows, there are also 2-morphisms (arrows between arrows), 3-morphisms, and so on, allowing for a richer structure that can capture more complex interactions. These higher dimensional structures are useful in various fields, including topology, homotopy theory, and theoretical computer science. They help mathematicians and scientists understand and model systems with intricate relationships, providing a framework for studying transformations and symmetries in a more comprehensive way.