die Neunziger
nineties
Refers to a decade, especially the years from 1990 to 1999. It is usually used in the plural.
Techno war die prägende Musik der Neunziger.
Techno was the defining music of the nineties.

nineties / nonagenarian
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nineties
Refers to a decade, especially the years from 1990 to 1999. It is usually used in the plural.
Techno war die prägende Musik der Neunziger.
Techno was the defining music of the nineties.

Words like 'Neunziger' (nineties/nonagenarian) are derived from numbers (here: 'neunzig' = ninety). This pattern is used for all decades, such as 'die Achtziger' (the eighties), 'die Siebziger' (the seventies), and also for age groups, such as 'ein Sechziger' (a person in their sixties).
Die Musik der Neunziger ist heute wieder populär.
The music of the nineties is popular again today.
You can recognize the meaning from the number: 'Die Neunziger' (the nineties), plural with the definite article, almost always means the decade. 'Ein Neunziger' (a nonagenarian), singular, refers to a person of that age.
In den Neunzigern gab es die ersten Mobiltelefone für alle.
In the nineties, the first mobile phones became available to everyone.
When the decade is meant, the word is usually used with the preposition 'in' (in) and in the dative plural: 'in den Neunzigern' (in the nineties). Phrases like 'Anfang/Mitte/Ende der Neunziger' (at the beginning/middle/end of the nineties) are also common.
Anfang der Neunziger zog meine Familie in eine andere Stadt.
At the beginning of the nineties, my family moved to another city.