Neutral safety switch: is a switch, usually on the transmission that "reads" whether the car car is in neutral or in gear.
If you hook up the remote starter through the switch it will fail to start the car if it "sees" that the car is in gear.
The switch works in a "open/closed" manner. If it is open the current (or ground/earth) will not flow through it, thereby not "allowing" the starter to engage. It may also work in the opposite way, meaning the switch must be open for the starter to engage.
This neutral safety switch is installed on most newer cars and works similar to the clutch pedal switch. The starter will not engage unless the clutch is pushed in. (On USA cars anyway)