The NACA duct get’s its name from the organisation that initially developed it, the National Advisory Committee for Aeronautics (NACA), an American organisation that predated NASA, and was eventually incorporated into NASA in 1958
The duct was designed with aerospace applications in mind, any amount of drag in these applications increases fuel consuption and limits top speed significantly, this makes minimizing drag critical. The NACA duct brings air into a vehicle with a very minimal increase in drag, this is one of the most common types of low-drag intake design, and when properly implemented, it allows air to be drawn into an internal duct, with minimal disturbance to the flow. The design was originally called a “submerged inlet,” since it consists of a shallow ramp with curved walls recessed into the exposed surface of a streamlined body, such as an aircraft. It is especially popular in racing car design.
The function of a NACA duct is to increase the flow rate of air through it while not disturbing the boundary layer. When the cross-sectional flow area of the duct is increased, you decrease the static pressure and make the duct into a negative pressure zone, but without the drag effects of a protuding scoop. The reason why the duct is narrow, then suddenly widens in a graceful arc is to increase the cross-sectional area slowly so that airflow does not separate and generate turbulance.
NACA ducts are useful in applications where air needs to be directed into an area which isn’t exposed to the direct air flow the scoop has access to. Quite often you will see NACA ducts along the sides of a car or engine bonnet. The NACA duct takes advantage of the boundary layer, a layer of slow moving air that “clings” to the bodywork of the car, especially where the bodywork flattens, or does not accelerate or decelerate the air flow. Areas like the roof and side body panels are good examples.