The installation of a cold air intake allows a larger volume of cooler dense air into the motor to produce higher more efficient power levels.
By reducing the temperature of the incoming air charge you increase the density of the air. Because cold air is much denser then warm air the cooler air holds more oxygen for any specific volume of air. So the more cold air you provide the more oxygen going into an engine equals the more powerful and efficient the combustion cycle is. A more efficient combustion cycle therefore produces more horsepower with improved fuel economy.