English Idiom: Give (someone) the green light
Have you ever had a great idea for a project at your company?
Perhaps you had to wait for a manager or boss to permit you to start the project.
If this has ever happened to you, then you were waiting for your boss to give the green light.
When someone gives the green light, it means that they are permitting someone to do something.
Maybe your child wants to go to Osaka-Jo Hall to see a concert. It will end late, and they will have to ride the train a long distance.
When they ask you if they can go, they are asking you to give the green light.