We used analogRead() to read the voltage on our potentiometer. The Arduino also has the opposite instruction: analogWrite(). This name is somewhat misleading. Unlike with an analog input, where a 10 bit A/D converter is used, the Arduino does not have a D/A converter on board.
The analogWrite() function uses a technique called Pulse Width Modulation. A digital output switches between HIGH and LOW in a fast pace, whereby the HIGH percentage is proportional to the analog value we wish to send out. If a device that receives the signal is too slow to follow the switching frequency, the result is it 'sees' the average of the on/off times. This also holds for light ... even though LEDs are fast enough to follow the switch frequency, our human eyes + brain are not and we see an average brightness.
Fun with Arduino 15 LED Dimmer, analogWrite(), Pulse Width Modulation