Distributed (a)synchronous computing.
A real world example could be an application-wide notification framework, which sends mails to the stakeholders at various points during the course of application usage. So the application would act as a Producer by create a Message object, putting it on a particular Queue, and moving forward.
There would be a set of Consumers who would subscribe to the Queue in question, and would take care handling the Message sent across. Note that during the course of this transaction, the Producers are decoupled from the logic of how a given Message would be handled.
Messaging frameworks (ActiveMQ and the likes) act as a backbone to facilitate such Message transactions by providing MessageBrokers.
