Suppose the hearer knows one person as “Zayd” and another description as “your brother,” yet does not know that the two descriptions apply to the same person. The speaker must choose which is being discussed and what new identity is to be supplied.
If Zayd is the established topic, «زَيْدٌ أَخُوكَ» is apt. If the brother is the established topic and his identity is sought, «أَخُوكَ زَيْدٌ» is apt.
The same reasoning works with other known descriptions. The listener may know the departing person without knowing his name. Definiteness of the predicate becomes meaningful because it connects what the hearer already knows with what remains unresolved.