"Της δείχνω το ποτήρι."
Translation:I show her the glass.
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It means that if you use a short-form pronoun before a verb to show an indirect object, you have to use the genitive form of the pronoun.
In Ancient Greek, it would have been dative, but the dative got lost and so its functions were assumed in some cases by either the genitive or the accusative... the former in the standard language but the latter in some dialects in the north.
(And in many other cases, including long-form pronouns or nouns, the dative is usually replaced by the preposition σε + accusative.)