RabbitMQ is an open source message broker software written in Erlang. It uses exchanges to route messages from producers to queues based on routing keys or bindings. There are four main exchange types - direct, fanout, topic, and headers. Mule can connect to RabbitMQ using the AMQP connector and exchange types to send and receive messages from RabbitMQ queues. For example, a Mule flow can use a direct exchange to send a message to a queue, while another flow receives from the same queue.