Pope St. Sylvester confirmed the Council of Nicea which condemned the Arian heresy. He oversaw the construction of the mother Church of Christendom-- the Basilica of Our Saviour, otherwise known as St. John Lateran. He governed the Church immediately following that period of severe persecution, lasting three hundred years, by the Roman empire.
As Dom Prosper Gueranger wrote:
So that Sylvester is messenger of the Peace which Christ came to give to the world, of which the Angels sang on Christmas night. He is the friend of Constantine; he confirms the Council of Nicea; he organizes the discipline of the Church for the new era on which she is now entering: the era of Peace. His predecessors in the See of Peter imaged Jesus in his sufferings; Sylvester represented Jesus in his triumph. His appearance during this Octave reminds us that the Divine Child who lies wrapped in swaddling-clothes, and is the object of Herod's persecution, is, notwithstanding all these humiliations, the Prince of Peace, the Father of the world to come.
Pontiff of Peace! from the abode of rest where now thou dwellest, look down upon the Church of God, surrounded as she is by implacable enemies, and beseech Jesus, the Prince of Peace, to hasten her triumph. Cast thine eye on that Rome which is so dear to thee, and which is so faithful in her love of thee. Protect and defend her Father, King and Pontiff. May she triumph over the wiles of political intrigue, the violence of tyranny, the craft of heretics, the perfidy of schismatics, the apathy of worldlings, and the cowardice of her own children. May she be honoured, loved and obeyed. May the sublime dignity of the Priesthood be recognized. May the spiritual power enjoy freedom of action. May the civil authority work hand in hand with the Church. May the Kingdom of God now come, and be received throughout the whole world, and may there be but one Fold and one Shepherd. Amen.
I can never mark this feast day without thinking of the final conclave and last Sovereign Pontiff in The Lord of the World, by Robert Hugh Benson. It is a good reminder to always trust in God's Providence in the face of the worst of worldly situations.