The significance of REST (Representational State Transfer) in web services architecture lies in its principles that enable easy communication between client and server applications over the web. REST employs standard HTTP methods, such as GET, POST, PUT, and DELETE, to manage resources effectively. This architectural style emphasizes stateless interactions, scalability, and uniform interfaces, making APIs more accessible and reducing complexity. By utilizing RESTful principles, developers can create robust and efficient web services that deliver a seamless experience for users and improve integration with diverse systems.