This Light reacts to a person touching it’s surface. Circuit traces printed across the surface of the lamp detect the resistance of the users finger and reacts by brighting or dimming the light.
This circuit uses two transistors in a Darlington pair to detect the slight bit of current that is allowed to run from a circuit trace to ground when a user touches the circuit. The chip then detects whitch circuit trace has been touched and changes the PWM signal on a pin accordingly to dim or brighten the light.
The PWM pin it attached to a large transistor that pulses a 12volt line that is applied to the Halogen bulb. the 5v arduino is just used to turn this transistor on.
check this page for lots of useful information and to find out how a Darlington pair works http://www.kpsec.freeuk.com/trancirc.htm