The significance of microservices architecture lies in its ability to enhance the development and deployment of applications. By breaking down a monolithic application into smaller, independent services, teams can develop, test, and deploy them individually. This leads to increased scalability and flexibility, as services can be modified or replaced without impacting the entire system. Additionally, microservices promote the use of different programming languages and technologies tailored to specific service needs, improving overall software resilience and facilitating continuous integration and delivery.