Sometimes this feast is called the Assumption, but this name is more prevalent in the Catholic West than the Orthodox East.
This feast commemorates the death (falling asleep: the literal meaning of dormition) of Mary, the Mother of God (Theotokos). It tells us that when she died, her soul was immediately taken up into heaven by Jesus Christ and that three days later her tomb was found empty,showing that her body had been resurrected.
There is no biblical basis for this feast, all of our knowledge of it comes from tradition. Of course, sceptics would say this is a myth, but there is a curious fact that supports the Orthodox tradition. That is the fact that, although several places in the Middle East claim to have the tomb of Mary, there is no tradition of the Theotokos being venerated in the tomb. In other words, there is no tradition of the veneration of her relics in any place. In the early church, when a holy person had died, the person’s relics were venerated in the tomb where they lay. There is not tradition of this in regard to the Theotokos.
But this feast has a real significance for us as believers and that is that she is the first human 
being that Christ resurrected from the dead, and this is to be our destiny also. Christ obviously rose first from the dead, but Christ is a divine person, so His resurrection and ours re somewhat different. The basic idea is this: when Adam and Eve sinned they and all humanity following them are subject to death. That is we all die. But this is not what God intended for us. He created us for an embodied existence, not simply for the survival of the soul. So when Christ died and rose again he freed all of humanity from the bonds of death. So at the end of time all human beings will be raised from the tomb to meet the last judgment.
The raising up of the Mother of God was the first example of what God intends for all of us, showing that the end of time death will be destroyed and all of humanity will live the eternal, embodied existence which Mary lives now.
*Although Christ raised Lazarus, the daughter of Jairus and the son of the widow of Nain, they lived a normal human life and died normally at the end of their lives.
Troparion — Tone 1
In giving birth you preserved your virginity, / In falling asleep you did not forsake the world, O Theotokos. / You were translated to life, O Mother of Life, / And by your prayers, you deliver our souls from death.
Kontakion — Tone 2
Neither the tomb, nor death could hold the Theotokos, / Who is constant in prayer and our firm hope in her intercessions. / For being the Mother of Life, / She was translated to life by the One who dwelt in her virginal womb.
Fr. John