This is the 4475th most frequent German word.
lateinische
"Lateinische" means "Latin" (adjective, relating to Latin language or culture).
Here, 'lateinische' is used as an adjective describing the noun 'Sprache' (language). It denotes something related to Latin.
Die lateinische Sprache hat viele europäische Sprachen beeinflusst.
The Latin language has influenced many European languages.
In this sentence, 'lateinische' again acts as an adjective, describing the type of 'Literatur' (literature), specifying that it pertains to Latin.
Sie studiert an der Universität lateinische Literatur.
She studies Latin literature at university.
Here, 'lateinische' is part of the compound 'spätlateinische', which means 'late Latin', indicating a specific historical period of Latin usage.