The Vonage Voice API is a tool for developers to integrate voice-calling capabilities into their applications, enabling features such as making and receiving phone calls, call control, text-to-speech and speech-to-text capabilities, interactive voice response systems, and more. To create a voice chatbot using the Vonage Voice API and OpenAI API, developers need a Vonage developer account, a Vonage phone number, an OpenAI API key, and to deploy their application on Vonage Cloud Runtime. The process involves deploying a new instance, customizing the code, and breaking down the call flow through various Java files that handle incoming events, speech recognition, error handling, and response generation.