Gender is simply one of three categories (nominally masculine, feminine and neuter) to which any noun belongs, which determines some grammatical features, in particular the endings of adjectives and determiners attached to that noun. Plural forms of adjectives and determiners, however, do not depend on gender. ‘Der’ is the masculine definite article, ‘das’ the neuter and ‘die’ the feminine one. ‘Die’ is also the plural form of the definite article for all genders. There is no comprehensive rule to determine the Gender of a certain noun a priori, so nouns are often memorised by learners in conjunction with the article to remember their gender. That said, there are some rules of thumb that can be very helpful at the beginning
Case is a value that a noun phrase takes on to indicate its grammatical function in the clause and/or sentence. The ending determiners, adjectives and—in a few cases—nouns take depends on their case, that is their role in the sentence. There are four cases in German:
The nominative case (Nominativ or Wer-Fall) is used for the subject of a clause (and also noun predicates referring to the subject), but it is never used after prepositions. It is also considered the unmarked or citation form of a word. ‘Der, die, das’ are the nominative singular forms of the definite article in German.
The genitive case (Genitiv or Wes-Fall) is used to indicate possession or relationship, it is also used with some prepositions. It corresponds more or less to English ‘'s’ or the preposition ‘of’.
The dative case (Dativ or Wem-Fall) is used to indicate the indirect object (in English sometimes expressed by the preposition ‘to’) of a verb and in conjunctions with many prepositions. It is also used to expressed the direct object of the so-called ‘dative verbs’. An example in which German would use the dative is ‘I give you my pen’ (‘ich gebe dir meinen Stift’). As you can see ‘you’ here answers the question ‘to whom (do you give your pen)?’.
The accusative case (Akkusativ or Wen-Fall) is used to indicate the direct object and in conjunction with various prepositions. An example where German would use the accusative is ‘I see the man’ (‘ich sehe den Mann ’) or ‘I give you my pen’ (‘ich gebe dir meinen Stift’). ‘den’ is the accusative masculine singular form of the definite article, for neuter, feminine and plural the accusative is exactly the same as the nominative (respectively das, die, die).
If you're interested in all the forms the article can take (depending on gender, number and case) you can click here, although it can be a little overwhelming at first, and it might be better to just learn the forms one by one as you come across the new cases.
One thing that I feel the need to specify, as it is an error often incurred by beginners: as I have already pointed out, nominative is also the case of ‘predicate nouns’. What this means is that nouns coming after ‘to be’ are not in the accusative because they are not a direct object. It is ‘
er is der Mann’ not ‘er ist den Mann’.
sächlich ( a thing/ child)
Don't confuse grammatical gender with natural gender.
Things can be grammatically masculine, feminine, or neuter -- for example, "the knife, the fork, the spoon" are das Messer, die Gabel, der Löffel. They're all things, but are not all grammatically neuter.
And der Junge (the boy) is grammatically masculine, even though a boy is a child.
Learn the gender together with the noun, as you usually can't guess it just from the meaning of the noun; you can't just go "male things are masculine" (e.g. a male victim is still a grammatically neuter das Opfer and a male person is still a grammatically feminine die Person) or "things are neuter".
Meaning-wise? Pretty much the same as in English (with some minor differences that you'll pick up on as you learn more).
If you're asking how to translate them: ‘der, die, das’ (masculine, feminine, neuter) is the definite article (‘the’), ‘ein, eine, ein’ (again, m., f., n.) is the indefinite article (‘a/an’) and it's the same word used for the numeral ‘one’ (used as an adjective, although ‘one’ used in counting is ‘eins’).
Why 'Der Junge', not 'Das Junge'?
Because those mean different things.
der Junge is "the boy".
das Junge is "the baby animal".
Are you trying to extrapolate from das Mädchen and das Kind, both of which refer to children, that all words referring to children are neuter? That's not how grammatical gender works in German.