It involved finding a place to plant the Chora trees. If they could do that, then the old times would be reborn anew and life would be good. This was after the Aiel/Tinker split. We find out about this in book 4, I think it was in the section about the birth of the Maiden sisterhood.

The Aiel were a cheerful people in the AoL. They sang and danced and lived and laughed. They were known for their singing. This all came to an end during/after the breaking. They stopped singing and their songs turned into a happy memory for better times. They broke off in order to leave behind their now meaningless responsibilities to the Aes Sedai and try to find some happiness in what they lost - singing and music.

They searched for music and found it. Nothing changed. Life still sucked. But they abandoned their final task, which must have brought guilt, because these are a loyal people - a group of people who even after 3000 years of violence, still hold to the way of the leaf. Their earlier 'betrayal' is like a grain of sand in an oyster.