Donatism was an early heresy. Named for its leader, the theologian Donatus the Great (d. 355), Donatism included a group of extremist sects, mostly in North Africa, that emphasized Asceticism. They valued martyrdom and found lapses of faith (even under torture or threat of death) inexcusable. The heresy involved their contention that the sacraments required a priest of pure moral character to be effective and only the pure (who had not lapsed under persecution) should be allowed in the church. They were opposed by Augustine of Hippo.
"The schism arose when certain Christians protested the election of the bishop of Carthage, charging that his consecration by Felix, bishop of Aptunga, was invalid because Felix was considered a traditor (i.e., one who turns over sacred books and relics to the civil authorities during a persecution). Condemnation was extended to all in communion with Felix. Behind their objection lay the heresy, familiar to Montanism and Novatian, that only those living a blameless life belonged in the church, and, further, that the validity of any sacrament depended upon the personal worthiness of the priest administering it. The Donatist practice of rebaptizing was particularly abhorrent to the orthodox. Condemned by the Synod of Arles (314) and also by the Roman emperor, Constantine I, the Donatists seceded (316) and set up their own hierarchy. By 350 they outnumbered the orthodox Christians in Africa, and each city had its opposing orthodox and Donatist bishops. It was the teaching of St. Augustine, as presented in his writings and at the debate between orthodox and Donatist bishops at Carthage (411), that turned the tide against Donatism. Strong state suppression and ascetic excesses among some of their own members further reduced their number. The remnants of the schismatic movement had vanished along with African Christianity before the advent of the Islamic invaders." (Excerpt from The Columbia Encyclopedia, Sixth Edition).