Theologically, the Donatists, named after their bishop Donatus, who . . . was their most articulate spokesman, parted company from wider Roman Catholicism in their theology of the Church. They disagreed with Cyprian (and subsequently with Augustine), who taught that the grace of the Holy Spirit was a function of the clerical office, not of the priests as people. The Donatists, on the other hand, believed that the presence of the Holy Spirit in a priest depended on his being in a state of grace himself. Clergy who were not virtuous (the traditores were the most obvious examples of those who had lost God's grace) could not properly baptise babies, turn bread and wine into the body and blood of Christ in the sacrament of Holy Communion, or ordain other clergy. Since everyone's salvation depended on receiving God's grace through baptism and Holy Communion, Donatists had to make very sure that each of their priests were in a state of grace themselves, and had been properly ordained by bishops who were also in a state of grace. Neither unworthy priests, nor priests whose ordination had failed because it had been performed by an unworthy bishop could give the people the sacraments on which their salvation depended.
Politically the Donatists repudiated the link between Church and State Constantine had forged. For them the government was a part of the worldly structures that were inherently opposed to Christ's Church.
This fierce opposition between the church and the wicked world led the Donatists to espouse an optimistic view of the church. As time went on the Donatists extended their conviction that the clergy needed to be holy and in a state of grace, to a view in which the entire church needed to be similarly holy and in a state of grace. They came to believe that the church was a church of saints, and that each member had to remain holy or face expulsion from the church.
The Donatists also became characterized by a cult of martyrdom. They longed for the final and greatest outpouring of God's grace, the death of the martyr, and greeted one another with the wish "may you gain your crown." [McManners ed., Oxford History of Christianity p. 43) They celebrated the anniversaries (called birthdays) of the death of martyrs. These became the earliest church calendars we know of.
Source:
http://www.bethel.edu/~letnie/AfricanChristianity/WNADonatism.html