"The sleeping people."
Translation:Det sovande folket.
Is it because this phrase refers with 'people' to a certain culture/society or why is personerna not correct?
No. That would equate to something like "That sleeping humans". You could say "De sovande människorna". Translating "People" in to Swedish can be complex, since there's several possibilities:
Folket (also "Folkslag") - Singular - People/Folk/Population/Group of people ("Det svenska folket" - "The Swedish people")
Människorna/Människor - Plural - People/Humans ("Människorna på gatorna" - "The people in the streets", "Människor behöver vatten" - "Humans need water", "Människor är konstiga"* - "Humans/People are strange")
Personer - Plural - People/Persons ("Hur många personer känner du?" - "How many people do you know?")
(*You could also substitute "Folk" for "Människor" in that sentence)
The way I think of it is that adjective needs a separate definite article in order to match the definiteness of the noun, similarly to how you use the -a suffix with plural adjectives to make them match the number of the noun.
What complicates things is that I believe there are circumstances where you don't use a den/det/de for the adjective, which I believe is one of those unfortunate things that you just have to pick up on a case-by-case basis. Perhaps a native Swedish-speaker can clarify.