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 patterns. There are four main exchange types - direct, fanout, topic, and headers. Mule connects to RabbitMQ using the AMQP connector. Flows in Mule can send messages to and receive messages from RabbitMQ queues via exchanges. For example, one flow may send a message to a queue using a direct exchange, while a receiving flow gets messages from the same queue via the direct exchange.