«زَيْدٌ أَخُوكَ»
Zayd is your brother.
The hearer may already know Zayd and the idea of his own brother separately without knowing they identify the same person. In that case the sentence conveys genuinely new information despite both expressions being definite.
«عَمْرٌو الْمُنْطَلِقُ»
ʿAmr is the one who departed.
Again, the hearer may recognize ʿAmr and the previously mentioned departing person but not know that the two descriptions pick out one individual. The information lies in connecting two known descriptions.