The genitive articles are roughly the equivalents of “the” and “a” when used to indicate possession or ownership and are also used with genitive prepositions.

In English, we indicate possession with an apostrophe-s or with the preposition “of”:

The cat’s pajamas or the pajamas of the cat

In German, this is expressed with the genitive:

die Pyjamas der Katze

Katze is a feminine noun, but takes der in the genitive case to imply ownership of die Pyjamas.

Masculine and neutral nouns take des and also a ~s or ~es ending:

der Kragen des Hundes
the dog’s collar

Like the German articles in other cases, the genitive articles also change depending on gender and plurality.