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 to send and receive messages. For example, one flow can send a message to a queue using a direct exchange, while another flow receives messages from the same queue using the direct exchange.