The significance of API versioning in software development lies in managing changes to application programming interfaces that may affect existing client integrations. Versioning allows developers to introduce new features, improvements, or fixes without breaking compatibility with older versions. This practice improves the user experience by providing a clear upgrade path and minimizing disruptions when changes occur. Proper API versioning strategies, such as semantic versioning, help maintain stability and ensure that consumers can continue using the API reliably, facilitating smoother transitions between updates.