Using Twilio with Salesforce allows developers to create interactive phone applications that integrate customer and user records from the CRM. By setting up a Visualforce page and using the TwiML Markup Language, developers can control live phone calls and respond to user input. The "Hello Monkey" example demonstrates how to use this technology to greet callers by name, while the second part of the tutorial shows how to connect calls to a second person or route them to a specific record owner. With this integration, businesses can create customized communication experiences that enhance customer engagement and support.