Iḍāfah (annexation) can identify the subject compactly. “كِتَابُ زَيْدٍ” (Zayd’s book) is often enough to pick out the intended book without a longer clause, making annexation one of the more economical routes to definiteness.
Iḍāfah can also evoke status. “عَبْدِي حَضَرَ” (My servant arrived) and “عَبْدُ الْخَلِيفَةِ حَضَرَ” (The caliph’s servant arrived) identify through different relationships; the second may draw attention to the caliph’s status as well.
Not every iḍāfah means ownership. Relations may involve association, specification, source or another connection justified by context.