A rhetorical question used by teenagers and young adults. to turn up is to get drunk or participate in other acts of debauchery, thus to turn down would be to become sober. It implies that the asker is drunk and will remain so the whole night. Made popular in recent singles by Snoop Dogg and Lil Jon, the only appropriate answer to such a question is "nothing".
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"Turn down for what?"
"My parents or the cops"
"Nope! Turn down for nothing!