1. grant permission to proceed with something
give the green light/go ahead to the project
In the same way that a green light at a set of traffic lights grants a car permission to move forward, a green light in this context gives permission for something to happen. It is typically used in a professional context, and is given by a figure of authority like a manager or a boss, often in relation to a project or proposal of some kind. Whether you are using the term 'green light,' or 'go-ahead,' it is essentially their approval and permission to proceed with something. A phrase with a similar meaning is 'sign off on.'