Mule ESB is a lightweight Java-based enterprise service bus and integration platform that allows developers to connect applications together quickly and easily, enabling data exchange between applications. It provides capabilities like service creation and hosting, service mediation, message routing, and data transformation to integrate existing systems regardless of technology. Mule ESB evaluates whether an ESB is needed based on factors like integrating multiple applications, supporting future application integration, requiring different communication protocols, and needing message routing capabilities.