In the Mafia, people whom have been made a 'made man' can't be killed without authorization from high ranking members, thus if anyone wants to whack a made man in the mafia, it's necessary for them to receive a green light before proceeding with killing them.
Green light is a term also used to put a hit on someone, if a gang member say someone has been green lighted, it means that the individual has a hit out for them. In 2014, Game, a rapper and Bloods gang member who's been feuding with rival Crip rapper '40 Glocc', posted a green light traffic light photo on his instagram page with the captions 'Green Light'. Many believe that was the Game's way of putting a hit out on 40 Glocc.
The term 'green light' is not used exclusively among criminals, it's often used by non-criminals to give the go-ahead. For instance, a project manager might give the green light to proceed with a project.