In a nutshell, the story concerns the attempts of Genom, a corporate conglomerate, to gain world power through its android creations (called "Boomers"). The Boomers (which are generally far more inhuman and lethal than the replicants in Blade Runner), are much like Terminators in that they can be covered with a outside shell that is human in appearance, and are often unleashed on the civilian populace to test their combat abilities. Although the AD Police has been created to handle illegal Boomer attacks, it is hindered by the government, whose strings are being pulled by Genom, and inadequate weaponry. It is thus left to the Knight Sabers, the protagonists of the series and a vigilante team, to combat the Boomers and thwart Genom's plans. The Sabers consist of four women who wear special combat hardsuits that rival Genom's technology, and include Priss (who provides most of the spunk), Sylia (the leader and a lingerie-shop owner whose father was an early android scientist killed by Genom, but managed to leave her his preliminary designs for the hardsuits before he was murdered), Linna (an aerobics instructor who, fittingly enough, is the most athletic of the group), and Nene (an AD Police dispatch officer who is a computer whiz and the group's main information-gatherer).
It may sound like standard action fare, but the above synopsis contains the basic groundwork of a cyberpunk piece: the collision of hard science (the Boomers vs. the hardsuits) and pop culture (Priss' hard rock tunes (which are probably Japan's equivalent of alternative guitar-feedback rock in the West)), the dystopia of MegaTokyo, filled with dark alleys, run-down highways, and brooding skyscrapers, with the Genom Towers (which look suspiciously like the Tyrell Corporation buildings from Blade Runner...) looming over the cityscape, a constant reminder of the domination of capitalism and technology, complex questions regarding the mixing of human and computer memory and the uncertain division between human and machine hiding under the cloak of sci-fi adventure, and Wagnerian operatics banging head to head with hard-boiled genre plots. In BGC these motifs and their presentation are at least as important as any story development.
Take the beginning of the first episode as an example of post-modern narrative fracturing: we are thrust into a montage which includes a performance by Priss with her band, the soon-to-be familiar faces of the Knight Sabers readying themselves for combat at various locations, and the AD Police fighting a losing battle against a Boomer on the loose. It is not until later that we begin to understand who the characters involved are, the general environment in which they live, and where the battle lines are drawn. Narrative in each episode is often fragmented and isolated, and an experience may be only understood after the fact; in nearly every episode, the full import of what we see as we enter the story in medias res is not comprehended until later.