Well, today it's eclipsed by the Eighteenth Sunday in Ordinary Time ... but, it's still a beautiful story.
This feast commemorates the miracle of the snowfall that occurred during the night of August 4-5 in the year 358 on the site where the basilica now stands. According to tradition, the Virgin Mary appeared in a dream to two faithful Roman Christians, the patrician John and his wife, as well as to Pope Liberius (352-366), asking that a church be built in her honor on the site where snow would fall on the night of August 4-5. Pope Liberius traced the outlines of the church in the snow and the first basilica was built on that site. It was completed about a century later by Pope Sixtus III (432-440), after the Council of Ephesus in 431 during which Mary was declared to be the Mother of God.More at Catholic Culture.
Check out the photos the Basilica by blogger and friend St. Liz who was in Rome a few weeks back.