The Order refers to a group of followers who worship the Evils. You learn about these people somewhat in the Diablo comic that is about the young man who finds Tyrael's sword.
Adria (who may be Lilith) had a child with Aidan while he was possessed by the soulstone of Diablo. This gave birth to Leah, who is Diablo's incarnation reborn in the realm of mankind. This is needed for invading the Heavens.
Azmodan, The Lord of Sin, and Belial, The Lord of Lies, were the two Lesser Evils who forced the three Prime Evils out of Hell. But while Azmodan thinks this was his plan and gave him control of Hell, it was actually all Diablo's plan to invade the Heavens. Hell's minions have never been able to get past the Diamond Gates and invade the Silver City.
So Diablo's plan was to create someone who could sneak past the Diamond Gate in the form of a human. But he needed someone to help put his plan in motion. This is where Belial comes in. Belial takes the form of a wise, old Horadric mage, Deckard Cain. It is Belial in the form of Cain who will guide the humans to do what is needed to be done to fulfill the prophecy. The start of this was getting Aidan to defeat Diablo and use the soulstone on himself. Adria, a follower of Diablo's, then has his baby, Leah. Cain then leads new hero's across the world to once again give the illusion that Diablo is defeated, while also putting an end to his two brothers, Baal and Mephisto, and destroying the Worldstone.
By destroying the Worldstone, it puts mankinds biggest support, Tyrael, in trouble with the Angiris Council. Imperius, Angel of Valor who originally wanted to destroy mankind, banishes Tyrael, Angel of Justice, to Sanctuary. That is the meteor. Imperius, now sets out to destroy mankind, and Tyrael is going to help the heroes of Diablo III stop him. Thus, Tyrael will lead the humans, including Cain and Leah, past the Diamond Gate and into the Silver City to stop Imperius. Only problem is that this directly leads to Diablo and Belial actually getting the chance to invade the Heavens. Diablo's plan all along.
...And, at the End of Days, Wisdom (Archangel Malthael) shall be lost
as Justice (Archangel Tyrael) falls upon the world of men.
Valor (Archangel Imperius) shall turn to Wrath-
and all Hope (Archangel Auriel)will be swallowed by Despair.
Death, at last, shall spread its wings over all-
as Fate (Archangel Itherael) lies shattered fover.
It's all about the fall of the Angiris Council and their destruction. Diablo with the help of Belial and us heroes have brought the Prophecy to happen.
So when you ask about The Order, I think it's actually the Order who follows the Evils. It's the Order who Adria was part of who has helped the Evils destroy the Heavens.