The article is talking about the possiblity of using a plant that glows as a sustainable light source (instead of street lamps, for example). Sustainable means that it does not hurt the environment. The title is saying that the readers of the website love the idea of using this glowing plant as a light source and want to see it in the real world. When they say "give...the green light", they are referring to a green stop light, which means go. They are saying that people want to go ahead with the idea. "The science stacks up" means the science is true and not just made up. So the statement "...and whether the science stacks up" is saying that people do not actually know yet if this will really work.