The significance of an API gateway in microservices architecture lies in its role as a centralized entry point for managing traffic between clients and backend services. It facilitates request routing, composition, and protocol translation, ensuring seamless communication among various services. The API gateway provides security features such as authentication and rate limiting, while also enabling analytics and monitoring. By simplifying interactions and reducing direct dependencies between services, it enhances maintainability, scalability, and performance of microservices-based applications.