The importance of API versioning in software development lies in its role in maintaining compatibility and stability. As applications evolve, changes to an API can impact users and other connected systems. By versioning an API, developers can ensure that existing clients continue to operate seamlessly while providing new features in newer versions. This practice allows for phased transitions to updated interfaces without disrupting service. Furthermore, it facilitates backward compatibility, ensuring smoother collaborations and integrations over time, which is essential in a rapidly changing software landscape.