Mule ESB is an open source integration platform that allows users to connect applications together and easily integrate existing systems regardless of technology. It provides key capabilities like service creation and hosting, service mediation, message routing, and data transformation across formats and protocols. Mule uses common components like filters, routers, transformers and scopes to route messages and make decisions. Core concepts include the Mule Expression Language for evaluating expressions and routing messages based on headers and payloads.