The Pax Romana is a period of roughly two centuries where there was relative peace and prosperity in the territory of the Roman Empire.
This peace and prosperity have made it much easier for the people to move throughout the empire, without being worried for their safety while on the road. The Christian missionaries used the opportunity, so they were able to travel without any concerns in lot of areas of the empire. While travelling, they were spreading the teachings of the Christianity, telling the people that the son of God has appeared in order to save them. Naturally, the people, especially the poor ones, were attracted to this new religion where there's someone that will save them and cares for them, so the Christianity managed to spread out relatively quickly across the continent.