It is not known exactly when Tertullian was born, but he was born in Carthage, North Africa, the son of a Roman centurion and the Empire. He was trained in law and apparently served as a jurist in Rome for a while.
We do not know how he came to faith, but he does seem to indicate in some of his writings that he was not always in the faith.
He is known only for his writings, which are many. Tertullian was a prolific writer and is the first of the Latin Fathers – the first Christian writer to write in Latin. His biblical quotations come from a Latin bible as well.
He is a master of the written word and penned some works specifically for the general educated public in defense of Christian faith. Some were written as open letters to the authorities arguing (as did Justin) against the persecution of Christians in the empire. His writings are terse, direct, and always attacking – as he probably argued in courtrooms, his aim is always to win the battle of the argument.
Tertullian had a fiery temperament and that contributed to some very strong disagreements with others in church leadership. The most serious issue is known “second repentance.”
Basically the church believed that after your initial repentance, baptism, and entrance into the family of faith you could not be formally allowed re-admittance to the church if you commit a “sin unto death.” Typically three sins were considered mortal sins: adultery, fornication, and apostasy (denouncing Christ during persecution).
During some of the more heated persecutions of the second century the faith of many believers failed, or “lapsed.” After the persecution calmed bishops found themselves with numbers of the lapsed desiring forgiveness and admission to the church. This number could be in the dozens in the major cities. As in any age, some bishops were more stern than others – some wanted to grant mercy to these penitent sinners. Others wanted to the church to hold to a high standard and demanded that lapsed believers could not be forgiven.
Tertullian falls into the rigorous camp, but the issue is not a simple one – he mainly felt that to go easy on an adulterer and to then hold someone at arms length whose faith held failed under torture was just wrong.