The Anti-Ori underground was a heretical group that existed within the Alteran Home Galaxy where they lived a shadow existence among the Human followers of the Ori and worked to save artifacts that predated their existence. They hoped to gather enough evidence to even convince the most devout of worshipper that the Ori are not what they claim to be.
Due to the fact that they were considered heretics, the group was careful in who they admitted within their organization. It was, however, wide spread and even included some of the monks within the City of Celestis. (SG1: "Avalon, Part 2", "Origin", "Crusade")
Vala Mal Doran joined this group while she was trapped in the Ori galaxy, but it took a lot to earn their trust. Their attempt to sabotage the Ori fleet failed and Denya and Seevis were killed while Vala managed to convince Tomin to spare her life. (SG1: "Crusade")
Later SG-1 went to them for help finding the Ark of Truth. Some of the members identities may be publicly known as Tomin, a former Ori Commander was able to locate Hertis to help them and they talked freely about the crusade in a bar. Hertis was suspicious of them, but once they took him to the Odyssey which was in orbit, he believed them. The valuable information he gave them led them to the Ark of Truth and ending the Ori crusade with the help of the Ascended Ancient Morgan Le Fay.
Their aims were completed when SG-1 found and used the Ark of Truth to spread the truth about Origin and the Ori were killed by Dr. Daniel Jackson with Merlin's weapon. Presumably they disbanded after this. (SG1: "The Ark of Truth")