Arduino Starter Kit, Color Mixing Lamp Project 4
If you look at the datasheet for the MCU at the center of the Arduino, the ATmega328, you'll see that it has 10-bit ADCs and 8-bit PWM (some can be 9- or 10-bit, but the Arduino libraries restrict them to 8).

Dividing the 10-bit ADC result (0 to 1023, 210-1) by 4 (22) scales it down to a 8-bit value (0 to 255, 28-1), which will fit in the PWM registers.