The angle that, if passed, will result in a rough pour into a glass from the carton. The chug line determines wether you will get a smooth pour or a rough pour into your glass.
If you are above the chug line or angle, the liquid escaping the container and the air entering the container will both be able to move through the mouth of the container at the same time. If you are holding a container below the chug line (lower angle) the ammount of liquid escaping exceeds the ammount of air entering, creating a vacume. Once this happens, air will rush into the container, pushing back the liquid. The process then repeats rapidly, creating an uneven pour or "chug".
If you want the best pour, stay just below the chug line.