In an iḍāfah construction, the first noun is the muḍāf and the second the muḍāf ilayh. In «غُلَامُ زَيْدٍ», the servant is identified by a relation to the known person Zayd.
Compare:
«غُلَامٌ حَاضِرٌ» — a servant is present; the individual is unspecified.
«غُلَامُ زَيْدٍ حَاضِرٌ» — Zayd's servant is present; relation supplies identification.
«هٰذَا الْغُلَامُ حَاضِرٌ» — a demonstrative identifies the person by pointing.
The point is not merely the juxtaposition of two nouns: annexation establishes an intelligible relation. That relation need not invariably mean ownership; its exact force depends on context.