In an objective genitive, the genitive noun is the object of the verbal idea contained in the noun it modifies; e.g. “the love of music” – where “music” is the object of the love. She loves the music. cf Smyth §1331
In a subjective genitive, the genitive noun is the agent of the verbal idea contained in the noun modified; e.g. “the love of her father” – where the love is exercised by the father. Her father loved her. cf Smyth §1330
See also GGBB p. 113 & 116.