The Mule Ajax connector allows asynchronous communication between a Mule flow and an external web page. It can be used as both an inbound and outbound connector. When configured as an inbound connector, it receives data from a JavaScript client attached to a web page. When configured as an outbound connector, it sends data to that web page without reloading the page. The Ajax connector configuration involves setting properties for the channel, address, encoding, and reconnection strategy. Transformers can also be applied to requests and responses.