After Cyprian of Carthage, son of a wealthy pagan aristocrat, became a Christian convert, he rose surprisingly quickly up the leadership ranks, so quickly in fact, that many were against his election as Bishop. When the persecution of Emperor Decius began, Cyprian and other Bishops fled Carthage after the highest Church leaders were quickly imprisoned and slain.
He was an important martyr in the history of the Church, and helped to maintain a sizeable community of Christians in Carthage despite serious imperial persecutions, one of which ended with his execution by beheading. He also articulated the importance of an organized ecclesiastical structure in the face of persecution.
For some of the reasons cited above, Cyprian was especially concerned with the issue of the unity of the church. This issue was especially important in the early church, since doctrinal disagreements were in some ways especially frequent then. Cyprian's writings on unity are still considered very important in the history of the development of the church.
Cyprian was an important writer in the Catholic Church. He wrote in Latin, and we can use his writings both to better understand Church history and to understand the history of his day. As others have mentioned, his election as Bishop was not universally accepted, and he was also persecuted under Emperor Valerian.
Interestingly, Cyprian was born a pagan to a wealthy family. He was a teacher before becoming a Christian, and he donated much of his wealth shortly after he was baptized around 245 A. D.
To the Catholic Church, Cyprian is a martyr. He was killed because of his unwillingness to compromise on his beliefs. It is interesting that at first he simply accepted exile, but then, after hearing of the executions of Christians including the pope, he returned to Carthage as a way of professing his faith and forcing the authorities to kill him.
Cyprian's election as bishop of Carthage was something that was opposed by various members of his community due to the wealthy background from which he emerged. Perhaps Cyprian is most famous however for his escape from Carthage in the face of the Decian persecution.