The best atrium definition is that of a room with a roof open displaying the sky, but as with most things architecture (or even art) the atrium definition has changed with the passing of time.
Originally, the atrium definition was that of an open roof to the sky in a rectangular shape, acting as the central, most important room in Roman architectural home design. By the third century B.C. the atrium house had become overwhelmingly popular in Italy, but its use gradually declined under the Roman Empire, when it was replaced by garden houses in everyone’s hearts.
Because of that, the atrium definition got a little broader: people started to refer to any open roof as an atrium; not only the rectangular shaped ones. Soon there were circular atriums and even odd shapes like stars for the ones with a more esoteric taste.
Cut to the twentieth century and atrium make its comeback because of two factors: shopping malls and ecological awareness. Looking to save up on energy costs, many shopping malls have atriums on their roof to bring in natural light and avoid having to light up the place with electric lights, and green architecture has catered to Off the Grid Homes by increasingly using atriums and other glass structures to improve natural lighting inside houses and reduce carbon emissions and the need to depend on the power grid and power companies.