It's similar to "the" in English here.
äpplen = apples
äpplena = the apples
bruna äpplen = brown apples
de bruna äpplena = the brown apples
I guess you need 'de' when an adjective is used and 'the' is used in the English translation (I'm guessing, I didn't study Swedish grammar, it's just my native language).
The noun it describes dictates the adjective. If the noun is an ett word, like ett djur (an animal) then use brunt, if it is an en word, like en hatt, use brun. Finally if it is a plural like äpplena, use bruna. A note here that a lot of the time adjectives ending in 'a' indicate plural