"Do you need my newspapers?"
Translation:Brauchst du meine Zeitungen?
When you make a mistake, Duo suggests you an acceptable sentence at random - not always the 'default' answer that you see when viewing the discussion page. The verb benötigen is a little more formal (kind of like "require"), but is an acceptable translation. The English sentence also doesn't make clear whether you're talking to one or more people, so any of the three "you" forms could be used in German.
It is the subject of the sentence. The person who "needs", not the thing needed.
Ich brauche dich : "I need you" Du brauchst mich : "You need me"
Incidentally it's similar to what happens in English for the 1st and 3rd person: I vs. me, he/she vs. him/her. In German it applies to the 2nd person as well.