Your lights are 12 volts, when not connected to shore power the lights are running on the battery and whatever voltage its able to put out (say around 12 volts). When you plug in shore power, your converter supplies a higher voltage (say around 14 volts) on the 12 volt line in order to charge your battery. The higher voltage will make your lights shine brighter.
2001 Coachmen Mirada (Ford F53 6.8L V10) - Toad 2001 Civic
It won't do MACH 2, but I can get a sandwich and take a pee.