The persecution under Diocletian required the handing over of scriptures and vessels, and clergy who complied were called traditores, those who handed over. When it ended, African Christians disagreed about whether such men could still function as clergy. The trigger was the consecration of Caecilian as bishop of Carthage in 311 or 312: his opponents held that one of the consecrating bishops had been a traditor, so the consecration was void and every act flowing from it was void too.
A rival was elected, and on his death Donatus succeeded him. He was an organiser of unusual force, and within a generation the church that took his name was the majority in Numidia and strong throughout the African provinces, with its own bishops in most towns and its own councils. Its position was not eccentric. It was the older African view, running back through Cyprian, that the holiness of the church is compromised by an unworthy minister.
What made it a lasting schism rather than a debate was the state. Constantine, newly favouring Christianity, referred the matter to a synod at Rome in 313 and then to the council of Arles in 314, both of which found for Caecilian, and imperial coercion followed the judgement. The African church was now divided along a line running through every town, and it stayed divided for three hundred years.