Most car stereo systems require a small amount of constant power. That is, connected directly to the battery. It's often used to keep clock circuitry running so it doesn't lose time every time you turn off your car. Usually it only uses a tiny amount of current, though, so it will not drain your battery very fast. However, REM stands for Remote, as I believe JimB suggested. I would assume that this is the trigger for any other amps you would have in the automotive. Basically, if you turn on the Amp, a small 12 volt signal would be sent from the REM wire into any other amps to signal them to switch on. If it is just this amp you're using, though, you do not need to connect the REM wire.
Regards,
Der Strom