Vonage Verify API` is used to implement a verification token system, which includes creating a verification request and checking if the provided code is valid. The `Vapor` framework is utilized for building the server-side application, with `SwiftUI` being used for the client-side application. A Vonage account is required to complete this tutorial as it provides the necessary API credentials. The project covers the creation of a server-side endpoint to receive verification requests and check if the provided code is valid using the Vonage Verify API. Additionally, it includes a client-side application built with SwiftUI that can test the server's functionality.