The genitive case is the "of" case in Latin, and its most common use is to show possession, often a noun possessing another noun (statua Claudiae, Claudia's statue), but also an author of a work (carmen Vergilii, the poem of Vergil), or even someone who has a certain quality (virtus Bruti, the virtue of Brutus).
cases first declension nouns second declension third declension