The Vonage Voice API is a Cloud-based service that enables developers to build high-quality voice applications, with features such as inbound and outbound call control, recording and storage, conference calls, and text-to-speech messages in multiple languages. To use the API, developers need to create a Vonage Application from the developer portal, set up webhooks using Node.js, and configure the application's settings. The tutorial covers how to receive inbound calls by implementing a webhook using Node.js, and provides an example of how to handle incoming requests and send text-to-speech messages. The Vonage Voice API is designed to be scalable and easy to use, making it suitable for building voice applications that can grow with the user's needs.