Again, outside of showing possession, there are some other uses of the genitive worth knowing/remembering. (Latin Declensions)
Genitive of the Whole
The genitive of a word which indicates the whole of something is used after another to word to show that non-genitive refers to a part of the whole of the genitive. Kinda hard to explain with words, but not with examples.
Pars urbis; part of the city (the city is the whole thing) Nēmō amīcōrum meōrum; (No one of my friends)
Continuing, the genitive of the whole is used with mīlia and after the neuter nom. and acc. of certain pronouns and adjectives.
nihil temporis (nothing of time) satis ēloquentiae; enough eloquence quid cōnsiliī; what plan?
Really, this usage makes sense when thinking of the genitive as the whole and these pronouns and adjectives as parts of that whole.