Twilio is a tool used for building conversations and can be integrated with IBM Watson's natural language processing capabilities to analyze and process real-time data. IBM's Bluemix platform allows developers to easily build and deploy apps using the IBM backbone and third-party API services like Twilio, enabling the creation of innovative IoT applications. The team from IBM showcased their cloud platform at Twilio's Signal Conference, demonstrating how IBM Watson can be used in a doctor's appointment scenario to analyze conversations and identify troublesome keywords in patient medical history.