This is the 10190th most frequent Polish word.
brudnych
"Brudnych" means "dirty" (plural or genitive form).
In this sentence, 'brudnych' is an adjective used in the genitive plural form to describe the noun 'talerzy' (dishes). This form is due to it being used in a negative sentence where genitive is required.
Brudnych talerzy nie należy zostawiać na stole.
Dirty dishes should not be left on the table.
Here, 'brudnych' is an adjective in the locative plural form matching the noun 'ubraniach' (clothes), showing a property of the noun within the context of the prepositional phrase.
Mówiła o swoich brudnych ubraniach z wakacji.
She talked about her dirty clothes from the vacation.
In this example, 'brudnych' is used in genitive plural to describe the noun 'powierzchni' (surfaces), again in the context of a negative imperative statement.