The Assumption has been believed and celebrated since the earliest times of Christianity. Today's feast was celebrated under various names (Commemoration, Dormition, Passing, Assumption) from at least the fifth or sixth century. Homilies concerning the Assumption go back to at least the Sixth Century. However, in order to make it a dogma of the faith meaning all Catholics must believe it, Pope Pius XII dogmatically declared Mary's Assumption into Heaven in 1950:
"... by the authority of our Lord Jesus Christ, of the Blessed Apostles Peter and Paul, and by our own authority, we pronounce, declare, and define it to be a divinely revealed dogma: that the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory" (Munificentissimus Deus) [Watch a video of the historic event]
Today is a Holy Day of Obligation as Catholics are required to attend Mass. For more information, see my post from 2005.