Mule ESB is a lightweight Java-based integration platform that allows different applications to communicate with each other by acting as a transit system for carrying data between applications. It supports over 30 protocols and technologies and includes powerful capabilities like acting as a single point of access, transaction manager, and security manager. Mule ESB uses flows to process messages where each message passes through a sequence of message processors like transformers, filters, routers, and components. Key elements of Mule messages include properties, variables, payload, and attachments.