Daniel B. Wallace (Greek Grammar Beyond the Basics, pp. 78-88) explains that in the case of the attributive genitive, "The genitive substantive specifies an attribute or innate quality of the head substantive. It is similar to a simple adjective in its semantic force, though more emphatic: it 'expresses quality like an adjective indeed, but with more sharpness and distinctness.'"
The last part of that quote is taken from A.T. Robertson's big grammar.
As Wallace points out, the genitive itself (whether possessive or descriptive, etc.) is grammatically substantival, but semantically adjectival; that is, the genitive functions like an adjective, although it is formally a substantive (i.e., a noun).
See Luke 16:9; Romans 6:6 for potential examples.