The significance of designing a modular architecture in software systems lies in its ability to enhance flexibility, maintainability, and scalability. A modular design breaks down an application into independent, interchangeable components or modules, allowing developers to work on specific parts without affecting the entire system. This approach makes it easier to update, replace, or scale individual modules as requirements change. Additionally, modular architecture fosters collaboration among teams, facilitates code reusability, and can lead to faster development cycles, resulting in more efficient and adaptive software solutions.