After Diocletian’s persecution of Christians, many of the later Roman emperors, including Constantine, saw Christianity as an ally instead of an enemy. In 313, when the only other emperor was Licinius, Constantine arranged an agreement between the two of them so that Christianity was no longer an illegal religion. This was known as the Edict of Milan. Later, in 323 when Constantine defeated Licinius to become the sole emperor, he made Christianity the preferred religion (which means he still allowed other religions, including emperor worship).
Constantine was not a theologically strong Christian, even waiting to be baptized on his deathbed with the belief that more sins would be covered, but he still had a large impact on the Christian movement. In the short term, the initial permissiveness toward the movement under cooperation with Licinius and the later preference allowed Christians to more openly profess their faith without fears of persecution. Chrisitianity was formerly in the public square in the form of executions, but now it was in the public square in the form of legal discourse.
In the long term, the effects were not so good. Constantine not only allowed Christianity, but he also wanted to govern it and proclaimed himself the bishop of bishops. This led to many decisions regarding the direction Christianity was to legally move in being made by someone who did not know much about Christianity. As an example, in the debate between Arius and Athanasius, Constantine changed his mind multiple times, always siding for the person he felt would bring the most peace among the people. He did not care about orthodox theology as much as he cared about politics and securing his own power. The good part of this incident, though, were the decisions that came out of the Council of Nicea which Constantine organized, regarding the divinity of Christ.
Although there was a bishop in Rome, where Constantine first lived, the idea that someone in Rome was to control the church was born with Constantine’s rule as head bishop. The bishop of Rome, though, was the bishop that was the most geographically close to Constantine so his opinion became elevated amongst the bishops due to this influence upon the emperor. The bishop’s influence became so elevated that when Constantine moved the capital of the empire to Constantinople, the Roman bishop was in the position to assume control over all of the other bishops. As the lectures indicate, there were many other factors that led to this and the eventual creation of the papacy, but this one cannot be forgotten.