For the earliest Christians, the preservation of their personal belief in God, as well as the preservation of the Church itself, was so important that they were willing to give their lives for it.
"Wherefore the Church does in every place, because of that love which she cherishes towards God, send forward, throughout all time, a multitude of martyrs to the Father; while all others not only have nothing of this kind to point to among themselves, but even maintain that such witness-bearing is not at all necessary" (Irenaeus, Adv. Haereses, IV, 33; emphasis mine).
This phenomenon of Christians willing to go to their deaths for their belief in Jesus Christ was astonishing to the Romans. More than that, the ability of certain Christians to freely die for the faith became a source of learning, growth, and encouragement for other Christians in the ancient world. That is why accounts of martyrdom were written down.
Among those that were widely circulated there seems to have been three basic forms (in this time period, we also see the beginning of a whole new form of literature in the Church, which we now know as hagiography): (a) those based on pro-consular records of investigation (e.g., Acts of Cyprian); (b) those based on witness accounts (e.g., Martyrdom of Polycarp); and (c) literary compositions completed by later writers. Thus, these stories ranged from the more or less accurate to the totally fictional (i.e., written like romances or legends).
Regardless of the form, however, each has a devotional purpose and character, which means that the accounts attempt not only to explain an event, but also to elucidate the theology of martyrdom as well as to inculcate a desire for devotional practice among readers. To illustrate this point, it seems that among all of these forms there was a stress laid on comparing the path of the martyr to the path that Jesus takes on the way to His own Passion. (This tendency can be found already in the Acts of the Apostles in the description of the martyrdom of Stephen.) In a parallel fashion, there was a similar stress placed on comparing the spiritual meaning of the martyr's path to that of the Passion again.
One of the best known stories of Christian martyrdom (outside of the New Testament) is that of Polycarp in the middle of the second century (The Martyrdom of Polycarp seems to be true. Irenaeus, in Adv. Haereses III, 3, 4 speaks of Polycarp "having reached an extremely old age, through martyrdom he rendered a most glorious and excellent witness." Branard believes in the authenticity of the Martyrdom of Polycarp in Kyriakon v. 1, pp. 193ff. Musurillo, in Acts of Martyrs, p. xiii, notes that the author of the account of the martyrs of Lyons (AD 177) knew about the martyrdom of Polycarp.).
From the account of his death, we get a real sense of the early theology of martyrdom. As a result, we also see that believers began to develop special devotions to the martyrs, who were considered to be perfect Christians that achieved union with Christ immediately upon death. These special devotions were eventually adapted into liturgical prayers that were recited at the tombs of those who were killed on the anniversaries of their deaths (in the case of Polycarp, his veneration also has to do with the fact that he was an elder of the Church. In other words, it isn't just the fact that he was martyred, but the fact that he was so righteous and was martyred).
In fact, some of these accounts spurred such a commitment among believers to live their lives only for Christ that it bolstered the desire for an ascetical life. The best of example of this is the life of St. Antony. St. Athanasius explains that the motivation for St. Antony’s decision to enter the monastic life was based partly on hearing passages from the Gospel According to St. Matthew. In other words, when St. Antony heard about those who literally took up a cross to follow Jesus, he embraced the ascetical life, which meant withdrawing from secular life to focus on manual labor, meditation on Scripture, and constant prayer. Stated differently, St. Antony chose a kind of self-inflicted martyrdom. While many of his predecessors were literally slain for their beliefs, St. Antony cut himself off from the conventional world. He saw this as a necessary facet to a life lived for Jesus Christ.
We are called no differently today.