After the tumultus start of Pope Boniface's papacy, the attack of the Visigoths on the city of Rome and the difficulties of having a number of short papacies back to back, it was time for a man of dignity (and longevity) take over the reign. This pope chose to uphold the rights of the Church and the dignity of the office.
Celestine was a native of Campagnia in Italy. We know his father was named Priscus and that he was a relative of the emperor Valentinian. He spent some time, as a youth, at Milan with St. Ambrose, who died in 397. The next time we hear about him is in a document written by Pope Innocent I in 416. There he is referred to as Celestine the Deacon.
In September, 422, Celestine was elected without opposition to the throne of Peter. His jurisdiction covered a decimated Rome, which had not yet recovered from the sack twelve years previous. Unfortunately, there was a sack on the orthodoxy of the Catholic faith going on at the same time. Celestine's good friend, St Augustine, was the first to ask for help, writing him a letter of congratulations and begging for help with Bishop Antonius of Fessula, Africa, who had been condemned by the African bishops but restored to his see by Boniface. Celestine agreed. But an outstanding dispute about the African priest, Apiarius, dragged on. Celestine espoused his cause and was confronted by a council of African bishops in 424 or 425, which denied a papal right of interference with their decision. This was not resolved until Pope Leo I, a few years later.
Another sack by heresy was the establishment of Novatian churches and a bishop in Rome. This heresy claimed that no one could forgive and absolve one who had committed a mortal sin. This, obviously, denies the mercy of God.. Although the sect had been condemned in 250, it was still a bone of contention 180 years later. The writer Socrates Scholasticus claimed "this Celestinus took away the churches from the Novatians at Rome, also, and obliged Ruticula, their bishop, to hold meetings secretly in private homes."
The Pelagian heresy, which originated in Britain, said that humans have the ability to do good without God's assistance and grace. This lead to the belief that one can attain salvation without help. Celestine knew this was dangerous for men's souls. He sent French priests, Germanus of Auxerre and Lupus of Troyes to Britain to eliminate this teaching. They were successful! Some years later, the pope sent Palladius to become bishop of Ireland. He lasted a year and died in Britain. One of the last acts of Celestine was to consecrate Patrick, student of Germanus, bishop of Ireland. This act is one of the farthest reaching acts of any pope in history, given what we know of Patrick's success. Due to Celestine's sending out missionaries to Britain and Ireland, he is considered the founder of the Vatican diplomatic service.
Celestine and Augustine, bishop of Hippo, were intimate friends. On the death of Augustine in 430, the pope heard that bishops of Gaul were speaking negatively about his friend's theology. He sent them a letter describing Augustine's sanctity, learning and zeal. As one contemporary biographer wrote, "For in the epistle which he wrote to the priests of Gaul, charging them with connivance with errors, in that by their silence they failed in their duty to the ancient faith, and allowed profane novelties to spring up, he says, 'We are deservedly to blame if we encourage error by silence. Therefore rebuke the people. Restrain their liberty of preaching!'" Celestine did not stand one iota of innovation from the Roman orthodoxy.
This pope's most well known achievement was condemning the Nestorian heresy at the Council of Ephesus. This heresy claimed that Jesus had two loosely connected natures, one divine, one human. It claims that Mary can only be the mother of the human and that her title, Theotokos, Mother of God, is not possible. We have several translations of his letters extant, explaining why Nestorius needed to be condemned for his teaching. And the man's condemnation was upheld.
In regards to the damaged churches still standing at the time of Celestine's election: He had two churches repaired, St. Maria in Trastevese and Saint Sabrina. He had the cemetary of Priscilla decorated with paintings depicting the Council of Ephesus. This is where he was buried shortly thereafter.