There are two important theological opinions on this question. Many church fathers in the West tend to believe the Virgin Mary experienced a real physical death, whereas many Church fathers in the East propose that she “fell asleep” (called the holy dormition) but did not actually die before leaving this earth. Though preserved from original sin in the womb of her mother, Saint Ann, through the Immaculate Conception, Mary nonetheless died because of the world’s loss of the preternatural gifts at the Fall. When Adam and Eve sinned, they lost certain gifts bestowed freely upon humanity. These gifts consisted of the following: intelligence (people did not have to learn by their mistakes), health (no one ever got sick or became old), agility (there was no pain in working or in childbirth), perfect balance in nature, and neverending life. These gifts were not due to our nature. Our bodies are prone to sickness and disease, so when these gifts were lost, they were lost for good.
Mary belongs to the human race. Though she was preserved, in the most perfect way, from original sin, she still experienced a world with the consequences of original sin—for instance, an imbalance in nature; storms, cold, and heat; bodies becoming sick; darkened intellects; and a need to study. So it is conceivable to believe that at the end of her life she died and then experienced the resurrection of the body and was assumed into paradise by her Son, Jesus Christ. In the Nicene Creed, we profess belief in the resurrection of the body, which means that after we die and the world comes to an end, our bodies will rise in their glorified states modeled after our Blessed Savior and His mother, Mary, and will be reunited with our souls. The doctrine of the Assumption meant that resurrection took place for Mary instantly; she did not have to wait until the end of the world, which would have been a punishment from original sin that Mary was preserved from.
The Eastern Church, such as Byzantine Catholic (in union with Rome) and Orthodox (Greek, Russian, etc.—not in union with Rome), professes belief in the “dormition (meaning ‘falling asleep’) of Mary,” which simply states that because Mary was preserved from original sin, she did not even have to die. Rather, at the end of her life on Earth, she simply fell asleep and then was assumed into paradise by the power of her Son. In Jerusalem there is the beautiful shrine and basilica of the dormition of Mary.
Both views are perfectly acceptable to believe. What is theologically important is the fact that she did not have to suffer the consequences of original sin since she was preserved from it at the moment of her conception, and therefore reigns in heaven as queen of heaven and earth.