The remote wire is the trigger for an amplifier.
If there is a factory amp, you will need to find out which wire is the amp's trigger. On my '04 Wrangler, it is a 20 gauge wire and the FSM calls it "Radio 12V Output". If he has an aftermarket amp, you would connect it to the amp's 12V + (usually labeled remote or REM +) trigger input terminal, next to the 12V + power input.
If there is no amp, you don't use the wire. Before buttoning everything up, make sure it works & that there is no exposed wire (cut clean & tape off) to cause a short.