The Great Diamond Authority also known as the Order of the Diamonds by Jasper, are a group of the matriarchs of the Gem Homeworld and are the main antagonists of Cartoon Network series Steven Universe.
Prior to the events of Steven Universe, there were four diamonds on the group before (Yellow, Pink, Blue and White). Later, the Diamonds began the colonization of several planets they encountered with earth being part of the colonization, Pink Diamond was in charge of complete successfully the colonization on the planet. However, one of her underlings, Rose Quartz shattered her and began a revolution against the Diamonds thus founding the Crystal Gems. Time passed and a war on earth started in which the Diamonds left earth to its fate by the Cluster and to make sure Rose and the Crystal Gems pay, they unleashed a corruption light across the planet which Rose and the remaining Crystal Gems (Garnet, Pearl and Amethyst) survived thanks to her shield.
Unfortunately for them, the remaining of their troops didn't get to escape and were corrupted along with the remaining Crystal Gems. Despite this, the Diamonds were aware the Cluster would eventually destroy earth getting rid of the Crystal Gems' base forever.
The Diamonds' presence was completely unknown during the first events of Season 1, but they finally get their mention by Jasper in "Jailbreak" when she says "Yellow Diamond needs to see this, thing". Their emblem is also shown in the Gem Warship without Pink Diamond on it.
In season 2, the diamonds' presence is limited with Jasper being stuck underwater with Lapis as the unstable fusion known as Malachite. Peridot is a recurring antagonist of the season and she is seen monitoring abandoned gem sites and attemptintg to contact Yellow Diamond and try to get off of Earth. Peridot is eventually captured by the Crystal Gems however and after she finally got in contact with Yellow Diamond, she ended up defecting from her and became a member of the Crystal Gems.
In Season 3, more information is found out about the Diamonds. In "Hit the Diamond", a group of five ruby soldiers from Homeworld are challenged to a game of baseball and they end up revealing that their real mission is to locate Jasper and go off to Neptune after Steven lied to them to find her. After being unfused from Lapis, Jasper begins assembling an army of corrupted gems to fight back against the Crystal Gems and has them all caged in the Beta Kindergarten. After Steven, Peridot, and Amethyst all find her, Jasper reveals that all gems are made to serve the the Order of the Diamonds (Great Diamond Authority) and that all gems who don't must be purged. She eventually fuses with a corrupted gem but it only lasts for a short period of time and she ends up being corrupted afterwards but not before she states that Rose had done something to Earth and Pink Diamond, her former superior and is then turned into a corrupted gem. Eventually, the five rubies return and Amethyst shape-shifts into Jasper and they go to the moon base where it's revealed that Rose Quartz had actually shattered Pink Diamond. In Bubbled, Steven and Eyeball are stuck in space and Eyeball reveals her intentions to kill Steven who she thinks is Rose to avenge Pink Diamond and return back to Homeworld as a hero but it fails and she's thrown back into space.