The Alteran Home Galaxy or Ori Home Galaxy is where the Alterans (the Ancients and the Ori) originated. However, after the Ori became a threat to them, the Ancients decided to abandon this galaxy in order to avoid war with their increasingly fanatical rival group. They later settled on many planets throughout Avalon (the Milky Way) including Dakara and Earth, the latter of which they called Terra.
Its exact location in the universe is unknown, but it appears to be very far from the Milky Way, since even the advanced Ori warships used Supergate travel (a massive Stargate big enough for ships to travel through) in order to get to the Milky Way instead of ordinary hyperspace travel. The Ancients picked the Milky Way because of its distance away from their home galaxy, so the Ori wouldn't easily find them. (SG1: "Counterstrike")
This galaxy was the birthplace of the Ancients and the Ori, which were known together as the Alterans. However, over time the two groups grew divided over their beliefs; the Ancients sought understanding through science and technology, while the Ori sought a spiritual answer. As the Ori grew more fervent in their beliefs, they attempted to destroy the Ancients. Unwilling to fight or expose the Ori as frauds, the Ancients fled the galaxy. With their departure, the Ori became the dominant power in the galaxy. Eventually, the Ori ascended, and learned that they could augment their already vast powers by convincing humans to worship them. They raised a group of human worshipers for this purpose, tightly controlling any evidence that life existed before them. Some of the humans from the galaxy formed a group called the Anti-Ori underground to expose the Ori as false gods. (SG1: "Origin", "The Pegasus Project", "Line in the Sand", "The Ark of Truth")
Dr. Daniel Jackson and Vala Mal Doran were the first humans from the Milky Way to discover the galaxy via Long-range communication device and their accompanying stones, believing that the Ancients actually went home rather than died or ascended. However, their efforts led the Ori to discover the Milky Way, and with their power sent Priors to our own galaxy to increase the number of believers to gain much more power to guarantee the Ancients' defeat. Just before Jackson and Vala burned to death for their "heresy", they returned to the Milky Way after the communication device was destroyed by the unstable vortex of a Stargate. (SG1: "Avalon, Part 2", "Origin")
Over the next few months, the Ori recruited an army to build space ships to carry out a crusade to wipe out all the unbelievers in the Milky Way and show their true power to believers in the Ori. They attempted to construct a Supergate so the ships could carry out the crusade. Fortunately it was destroyed, but Vala traveled to the galaxy to the planet Ver Isca, where she spent her time there joining the underground and marrying Tomin, who became a soldier. She eventually returned to the Milky Way. (SG1: "Beachhead", "Crusade", "Camelot")
In 2007, SG-1 sent the Sangraal through the Supergate to kill the Ori. The plan worked, though Adria ascended and took all the power for herself. SG-1 later traveled to the galaxy by Supergate on Odyssey to retrieve the Ark of Truth and ended up using it to spread the truth of the Ori to the people of that galaxy. The device was activated, and all the Priors saw the "truth", leaving every human in the galaxy to denounce the Ori. This weakened Adria, allowing Morgan Le Fay, an Ascended Ancient to destroy her at the cost of her own life. Later, the Ark of Truth was used to expose the people of the Milky Way to the truth about the Ori through a captured Prior and the Ori army retreated back to this galaxy under the command of Tomin, ending the crusade. (SG1: "The Shroud", "The Ark of Truth")