Determiners precede the noun and specify it. They answer the basic question "Which one?". The class of determiners includes indefinite/definite articles, demonstrative adjectives and possessive adjectives.

The Indefinite Article

In Spanish, the indefinite article refers to a noun that actually 'exists' in the context, it is often omitted when the noun refers to a simple human classification (especially after words like ser) or to an abstract modifier of classification (especially after a preposition like de). Compare the following sentences:

Arturo es un profesor alemán. [modified] Arturo es profesor. [simple classification]
'Arthur is a German professor.' 'Arthur is a professor. '

Esta es la ropa de un niño. Esta es ropa de niño. [type of clothing]
'This is the clothing of a [existing] child.' 'This is child's/children's clothing.'

Certain limiting adjectives do not take indefinite article: otro, mil, cien, cierto, tal

The Definite Article

Like English, the Spanish the definite article is used to refer to individuals or to a specific set of individuals. Unlike English, Spanish uses the definite article to refer to a concept in its totality. English uses zero-article to express this notion. Compare these sentences:

El gato tomó la leche. 'The cat drank the milk.' [indvidual]
Los gatos se escaparon. 'The cats escaped.' [specific set]
Los gatos son independientes. 'Cats are independent.' [totality/all cats]
Odio los gatos. 'I hate cats.' [totality/all cats]

Rule of thumb: Subject nouns in Spanish require a determiner [an article, a demonstrative adjective, or a possessive adjective.]

There are a number of specific cases where Spanish uses the definite article, but English does not. A few important ones are: titles in indirect reference [el señor Juárez = 'Mr. Juarez'], days of week (except after ser) [Vamos el lunes. = ' We are going on Monday.'] , clock time [ Son las tres. = 'It is three o'clock.'], in place of the possessive adjective [Se quitó la chaqueta. = 'He took off his jacket.'], etc.