For the Catholic Church, the Assumption of the Virgin Mary is a dogma (i.e. a truth of the faith which has authority, so that one cannot affirm to be Catholic without adhering to that truth).The dogma of the Assumption was proclaimed by Pope Pie XII in 1950. Here is a passage from article 966 of the Catechism of the Catholic Church which recalls the content and the meaning of this dogma:
“Finally, the Immaculate Virgin, preserved free from all guilt of original sin, on the completion of her earthly sojourn, was taken up body and soul into heavenly glory, and exalted by the Lord as Queen of the universe, that she might be the more fully confirmed to her Son, the Lord of lords and the conqueror of sin and death” (Lumen Gentium §59).
“The Assumption of the Blessed Virgin is a singular participation in her Son's Resurrection and an anticipation of the resurrection of other Christians…” (CEC § 966).
Long before the promulgation of dogma, Christianity believed in the Assumption of the Mother of God and celebrated it
Actually, long before the promulgation of dogma, Christianity believed in the Assumption of the Mother of God and honored it with a feast day. As Mgr Michel Dubost (a French bishop) writes in his book "Marie" (ed. Mame, Paris 2002):
"The Feast of the Assumption began in Jerusalem, but it is difficult to know when. The origin of the feast perhaps comes from the consecration of a church dedicated to Mary in Kathisma by Bishop Juvenal (422-458). (Kathisma is the presumed stopover place of the Virgin between Nazareth and Bethlehem.) But its origin more likely comes from the consecration of another church in Gethsemane, next to Jerusalem in the sixth century.
“Nevertheless, the feast spread to the entire Empire through Emperor Maurice (582-602) under the name of the Dormition of the Virgin Mary. It has always been celebrated on August 15. The Oriental liturgical year begins on September 1st with the Nativity of the Virgin on September 8th and ends with her entry into glory on August 15th.”