The Greek definite article (ὁ, ἡ, τό) is more versatile than English "the."
Uses of the article: • Definite: ὁ ἀνήρ ("the man") • Generic: ὁ ἄνθρωπος ("mankind", humans in general) • With proper names: ὁ Σωκράτης ("Socrates") • With abstract nouns: ἡ ἀρετή ("virtue") • Substantivizing: τὸ καλόν ("the beautiful", "beauty") • With participles: ὁ γράφων ("the one writing") • With infinitives: τὸ γράφειν ("writing", "to write")
The article agrees with its noun in gender, number, and case. Greek has no indefinite article; "a man" is simply ἀνήρ.