What is the difference between nominative, accusative and dative?

The nominative, accusative and dative are cases: they affect adjective endings and the article used for a noun.  The nominative is used for the subject, the noun which is carrying out the action. In the sentence 'Die Frau gibt dem Mann das Geschenk.', the woman is the subject and therefore takes the nominative. The article used is 'die' as the noun is feminine and in the nominative.  The accusative is used for the direct object: the person/thing the verb is acting on- this is the present, the present is the thing being given. The article used is 'das' as the noun is neuter and in the accusative.  The dative is used for the indirect object, something affected by the verb but not directly being acted on: this is the man, the present is being given to him, it is not him who is being given.  The article used is 'dem' as the noun is masculine and in the dative.