A delayed green light means that traffic stopped on one side of an intersection with a traffic signal get the green light to proceed prior to the traffic on opposite side of the intersection. Traffic on both sides get a green light; the delay just means that one side moves prior to the other.
Traffic engineers install a delayed green light due to traffic volume moving through the intersection. Prior to the installation of the traffic signal, an engineer conducts a traffic study to determine the time of day, the number of cars and the direction that each car is traveling as it moves through the intersection. A delayed signal is one solution if the traffic study indicates that the amount of traffic moving through one side of the intersection is much larger than traffic moving in the opposite direction. To avoid a large backup of traffic on the busy side of the intersection, the engineer adjusts the traffic signal so that cars on that side of the intersection have more green time. This is important for the cars turning left from the busy side. More green time allows the vehicles that are turning left to move through the intersection without conflicts with oncoming traffic.