The Twilio API for WhatsApp allows users to send and receive media messages, including images, audio files, and PDFs up to 5MB. To use this feature with Node.js, developers need a Twilio account, Node.js, and a package manager like npm installed, as well as an environment variable set for the Account SID and Auth Token. The process involves installing the twilio helper library, creating a new file with sample code, and running it to send the first media message. However, there are differences between MMS and WhatsApp media messages, including limitations on file types and session duration, which should be taken into consideration when using this feature.