The significance of API management in software development lies in its ability to streamline the creation, deployment, and monitoring of APIs. It ensures that APIs are usable, secure, and efficiently connect different software applications. Good API management allows organizations to manage usage, monitor performance, and enforce security protocols, thus fostering integration within their systems. Additionally, it supports scalability, enabling businesses to adapt their services and innovate faster while engaging third-party developers to extend functionality and enhance customer experiences through a robust application ecosystem.