Greek nouns have 3 distinguishable features, namely number, case, and gender.
Number is defined as either singular or plural (plus a rarely used dual).
Case indicates grammatical relationships of nouns within a phrase or sentence. Where Indo-European used 8 cases, Classical Greek employs 5 distinct cases, thus causing some Greek cases to serve more than one function:
Nominative, for the subjects of verbs, predicate nominatives and naming of objects.
Genitive, for nouns that (1) describe things like possession/dependence and (2) provide movement “from”. The Genitive is used where in English the proposition “of” is found.
Dative, to describe (1) interested parties, (2) the position/time at which something occurs and (3) instrumentality. The Dative is used where in English the propositions “to”, “for”, “by”, “with”, “in” or “at” are found.
Accusative, for nouns that describe direct objects, motion towards another object or the length of space and time.
Vocative, for nouns being directly addressed.
Gender is either feminine, masculine or neuter. The terms feminine and masculine are grammatical distinctions, not sexual distinctions. However, usually terms for living things that are male are in the masculine gender, while terms for living things that are feminine are of the feminine gender. Gender is also closely related to the declension of many nouns. Gender cannot be guessed with regularity and so must be memorized as a core component of a Greek noun.