The Alteran division was a difference of philosophical viewpoints that lead them to a schism among the unified Alterans, splitting them into the Ori who were devoted to religion and the group that would later become the Ancients who were devoted to science.
The lower planes
Millions of years ago, the Alterans were the first evolution of humans, on an evolutionary path to Ascension. However, a philosophical division emerged. Those who came to be called the Ori grew more fervent in their religious belief, while those who came to be known as the Ancients, who still called themselves the Alterans, came to "believe" more in science. Eventually, the Ori became so extreme that the two factions began to oppose each other, culminating in the Ori trying to wipe out the Ancients. To avoid a war, the Ancients left the Alteran Home Galaxy and arrived in the Milky Way.
Even with the distance of millions of light years, the Ori held deep hatred for the Ancients. Dr. Daniel Jackson has speculated that the pre-ascended Ori were responsible for the Ancient contagion that wiped out the Ancients in the Milky Way and caused them to leave for the Pegasus galaxy in Atlantis. (SG1: "Avalon, Part 2", "Origin", "The Fourth Horseman, Part 1", "The Fourth Horseman, Part 2")
The higher planes
Even when both factions ascended, they continued to oppose each other. The Ori created a new evolution of humans and passed down a religion called Origin, which placed them as the creators of the universe and promised to ascend those that "followed the path", and destroying all who rejected it. In actuality, Origin was intended to channel the energy from their followers to the Ori via a complex metaphysical process which essentially drains their followers of power. The Ancients consider this a death of the most meaningless kind, as there is no attempt to achieve enlightenment outside of Ori teachings. Because of this, the Ancients have adopted a strict policy of non-interference with the lower planes, feeling that interference for any reason would make them no better than the Ori. However, the Ancients are believed to have associated demonic and evil connotations with fire, the central icon of Origin, to influence those in the Milky Way galaxy to reject it.
Even though the Ori's ultimate goal is the destruction of the Ancients, the Ancients will only intervene on the plane of existence they share with the Ori, and even then it is only if the Ori significantly break the rules (such as destroying the Milky Way.) The Ancients, though opposing the Ori in every way, are unsure if a conflict on that level would result in victory, as well as feeling that conflict would not be the best choice for further enlightenment.
Moros, the last High Counselor of Atlantis, realized the threat the Ori could one day pose, so he descended himself, retaining all of his knowledge and some of his powers, to create a weapon to destroy ascended beings. He entrusted some of his secrets to the Tau'ri monarch Ambrosius Aurelianus, known as King Arthur. To Arthur and his noblemen, the Knights of the Round Table, he became known as Merlin. Moros' weapon came to be known as the Sangraal. However, the Others feared a weapon which could be used against them. They sent Ganos Lal to observe him, destroy the weapon, and, if necessary, kill him. Ganos became known to the Tau'ri as Morgan Le Fay. She managed to destroy the weapon and kidnap Merlin, causing Arthur and the Knights of the Round Table to go on a quest for the Sangraal. However, Morgan had come to believe that Merlin was right about the threat of the Ori, but knew the weapon was too dangerous to preserve. Morgan then placed Merlin in a stasis pod, hoping to preserve him for when the time came to destroy the Ori. (SG1: "Avalon, Part 2", "Origin", "The Fourth Horseman, Part 1", "The Fourth Horseman, Part 2", "Arthur's Mantle", "Camelot", "Morpheus", "The Pegasus Project", "The Quest, Part 1", "The Quest, Part 2")
The Crusade into the Milky Way
The conflict reached a new level when Dr. Daniel Jackson and Vala Mal Doran alerted the Ori to the presence of Humans in the Milky Way, whom the Ancients had hidden. Nearly a year later, the Ori Army managed to enter the Milky Way, hoping to convert enough humans to build up their power and destroy the Ancients. To insure that they would also be able to circumvent the rules of the higher planes, reducing the chances of the Ancients attacking them before they had built up enough power to ensure victory, one of the Ori allowed herself to be reborn in Vala Mal Doran, allowing one of the Ori to lead their armies as the Orici without intervention by the Ancients.
However, even a conflict on that level would have been extremely costly, and the Ori seemed unwilling to risk their collective skins. Knowing that SG-1 had learned of the Sangraal, the Orici, known as Adria, lead SG-1 to the planet where she believed the Sangraal was. SG-1 was transported to another planet, and awoke Merlin, who then began working on another Sangraal. However, Merlin's body had aged too much during stasis, so he transferred his memories and some of his powers to Jackson, who, to give SG-1 a chance to escape, allowed himself to be captured by Adria.
Merlin was able to protect Daniel's mind as Adria tried to convert him, and protect him when he became a Prior. Daniel claimed he would complete the Sangraal for the Ori to use against the Ancients, but he really intended to send it to the Alteran Home Galaxy through a Supergate. Allowing himself to be captured by SG-1, he convinced them to help, and ultimately sent the charging Sangraal to through the Supergate. Although the Ori were destroyed, their followers simply believed they had abandoned them due to their failing to conquer the Milky Way, and that they must prove themselves. They sent another six Ori warships through the Supergate to the Milky Way. Eventually, Adria was captured by Ba'al, and taken as a host. SG-1 attempted to remove Ba'al and replace him with a Tok'ra, but Ba'al released his symbiote toxin into Adria. Dying, Adria used the time remaining to successfully ascend.
The fall of the Ori
Adria assumed all the power the Ori once held, although, it also means that Adria can no longer interfere on the lower planes without inciting the Ancients wrath. SG-1 managed to strip her of a lot of her power by using the Ark of Truth to reveal the truth to her followers in the Ori galaxy and Morgan Le Fay, who had been secretly helping the team all along engages her in battle and the two apparently destroyed each other, suggesting that a single Ancient was more powerful than an Ori as Adria did still have many followers in the Milky Way to boost her power to equal Morgan's. The Ark was then used to spread the truth in the Milky Way, ending the Ori crusade for good. (SG1: "Avalon, Part 2", "Origin", "Arthur's Mantle", "Crusade", "Camelot", "Flesh and Blood", "The Pegasus Project", "Counterstrike", "The Quest, Part 1", "The Quest, Part 2", "The Shroud", "Dominion", "The Ark of Truth")