The Solemnity of the Assumption of the Blessed Virgin Mary is a solemnity and Holy Day of Obligation, celebrated on August 15th that remembers the bodily taking up of Mary into Heaven.
In his Apostolic Constitution Munificentissimus Deus (The most bountiful God) issued in 1950, Pope Venerable Pius XII invoked papal infallibility and formally defined the dogma of the Assumption:
We proclaim and define it to be a dogma revealed by God that the immaculate Mother of God, Mary ever virgin, when the course of her earthly life was finished, was taken up body and soul into the glory of heaven
As early as the fourth century the discussion of immortality of the Blessed Virgin Mary was already fairly widespread. Epiphanius of Salamis suggested that the Woman clothed in the sun in Chapter 12 of the Book of Revelation was a reference to her immortality. Saint Epiphanius, Tychonius, Quodvultdeus, Cassiodorus, Andreas of Caesarea and Oikoumenios all agreed with this interpretation. By the 8th century Saint John of Damascus wrote out what had become the standard Eastern tradition:
St. Juvenal, Bishop of Jerusalem, at the Council of Chalcedon (451), made known to the Emperor Marcian and Pulcheria, who wished to possess the body of the Mother of God, that Mary died in the presence of all the Apostles, but that her tomb, when opened upon the request of St. Thomas, was found empty; wherefrom the Apostles concluded that the body was taken up to heaven
Pope Sergius I in the 9th century celebrated the Assumption and Pope Leo IV officially confirmed the feast for celebration. Pope Venerable Pius XII wrote in his constitution several Sacred Writings helped form the basis for his defining including:
1 Corinthians 15
While the Roman Catholic Church celebrates the Feast of the Assumption, the Eastern Orthodox and Eastern Catholic Church celebrates the Dormition of the Mother of God or the Dormition of the Theotokos (The falling asleep of the Mother of God) on the same date. The Eastern celebration, however, is preceded by a 14 day fast. The other difference between the two is that the Roman Catholic Church has not dogmatically defined whether Mary first died before the assumption or that her body was assumed into Heaven without first dying whereas the Eastern tradition hold's tight to a bodily death before the Assumption.