This feast commemorates the rededication of the church by Pope Sixtus III just after the First Council of Ephesus.
This council was called to answer the problems caused by the teachings of Nestorius. Nestorianism split the natures of the Christ into human and divine. So while believing that Jesus was God, it denied that Mary was the mother of God. Cyril contested this belief, and at the Council it was declared that Mary was indeed the Theotokos, the birth giver of God.
This church is also called the Church of Our Lady of the Snows. It is said that in the forth century, during the pontificate of Liberius, a Roman patrician named John and his wife, who were without child, pray to the Virgin Mary, that she might make known a way that they might dispose of their property in her honor. On August 5th, in the heat of the Roman summer, snow fell on the Esquiline Hill. The couple had a vision of this event, and on the spot on the hill side which had been covered with snow they built a church.