The JMS specification defines the durable subscription. Basically, it is used when a subscriber needs to receive all the messages published to a topic, even those which are sent while the subscriber is off-line. Here is a quote from JMS 2.0 specification:
"A durable subscription is used by an application that needs to receive all the messages published on a topic, including the ones published when there is no consumer associated with it. The JMS provider retains a record of this durable subscription and ensures that all messages from the topic's publishers are retained until they are delivered to, and acknowledged by, a consumer on the durable subscription or until they have expired."
Durable subscription is often used for the Notification message exchange pattern. For more information about the Notification message exchange pattern, see Notification.