The Feast of the Assumption of the Blessed Virgin Mary marks the end of Mary's earthly life. Pope Pius XII, in Munificentissimus Deus (1950), defined that Mary, "after the completion of her earthly life was assumed body and soul into the glory of heaven." Being born without sin, she may have been taken into heaven in whole, without dying, body and soul uncorrupt. The Orthodox Christians refer to the Assumption as the Dormition of Mary, of the 'Falling Asleep'. They believe that Mary suffered earthly death, but was taken into heaven immediately. Either assumption is possible (pun intended), because the key thing to note is that her body and soul were left uncorrupt and taken into heaven.
Obviously, there is no biblical evidence for this, but this is based on history and the tradition of the Church. In the early Church, the relics and remains of the saints were venerated. However, there have been no records relating to the remains of the Blessed Virgin Mary. If they existed, many would have tried to claim them, but nobody did.
The Assumption is a fitting earthly ending for Mary, for being concieved without sin makes this Assumption a natural and most logical conclusion. Our earthly deaths are the result of sin, but she was sinless. Furthermore, she is the Mother of God, the most perfect example for all Christians. Her Assumption is a reminder to all of us that at the Final Judgement, our bodies and souls shall be reunited to rejoice in Earth, or God forbid, suffer in Hell. May Her example and prayers lead us to Christ our King and Redeemer. Venite Dominus Iesus!
One last thing to take note. There is a difference between Jesus' Ascension and Mary's Assumption. Jesus is God, and He rose to Heaven by His Power. Mary though perfect, remains God's creature. Therefore it was God who lifted Her up, not Herself. for 'He puts down the proud hearted and raises the lowly.
http://en.wikipedia.org/wiki/Assumption_of_Maryhttp://www.newadvent.org/cathen/02006b.htm