The persecution under Decius in 250 required everyone in the empire to sacrifice and to obtain a certificate, a libellus, proving it. It was designed to catch a whole population rather than to identify a few, and it worked. In Carthage very large numbers complied, some by sacrificing and some by buying a certificate without sacrificing. Cyprian himself withdrew from the city and governed by letter, which his critics used against him afterwards.
When the pressure lifted the question was what to do with them. Confessors, those who had been imprisoned and had not given way, began issuing letters of peace readmitting the lapsed on their own authority, which Cyprian regarded as a collapse of order. At the other extreme a party at Rome around Novatian held that the church had no power to readmit them at all.
His answer, worked out in De Lapsis and in a series of African councils, distinguished degrees. Those who had sacrificed were treated more severely than those who had merely bought a certificate, penance was graduated by what had been done, and readmission was a decision of the bishop with his clergy and people rather than of an individual confessor. The principle underneath is the one he is remembered for, that the unity of the church is not an optional good but the condition of everything else it does.