Today, we remember the Virgin Mary's repose. Her being a child of Adam, she still carried with her the consequences of a fallen world, even if she herself never personally sinned.
The account of her dormition ("falling asleep") starts with her visiting the site of her Son's death, Golgotha. There, the Angel Gabriel appeared, presented her with an olive branch, and told her that her repose is impending. From there, she went to Bethlehem, and asked for the Apostles to arrive.
All the Apostles (even those dead) arrived, save Thomas, to celebrate her life and repose with her. As they were singing, she passed away as peacefully as falling asleep. Then the light of God shone down on her, and Christ Himself came down and carried the Virgin Mary's soul up to Heaven. Her body was then buried.
During her burial procession, the unbelieving Jews tried to interrupt it, even going so far as to burn everything with fire. Some were struck blind. One of the Jewish priests, Athonios, got close enough to try and topple the body of the Virgin Mary from the procession, but when he touched her, his hands were cut off by an angel. This event caused him to fall down in repentance and was a fervent follower of Christ from that moment on.
Two days later, Thomas arrived from India. When he arrived, he told the Apostles a marvellous story. He told them that when he was on his way, he witnessed the body of the Virgin Mary being taken to Heaven, following her soul's departure. (This is the portion of the feast the Latins emphasise, often to the point of forgetting that she did die first. The Catechism of the Catholic Church vaguely says "when the course of her earthly life was finished" and only in a footnote quotes the Troparion which mentions her falling asleep. (CCC 966))
Reversing his infamous doubt, the other Apostles doubted Thomas's story. They opened her tomb and indeed saw that it was empty.
Her death, as in life, points us to Christ. Her death shows us how to we are to have a "Christian ending to our lives (Divine Liturgy of St. John Chrysostom)," and ultimately the final resurrection we will all share in, as she already has.
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.