The Assumption

 

"All-powerful and ever-living God: You raised the sinless Virgin Mary, mother of your Son, body and soul, to the glory of heaven. May we see heaven as our final goal and come to share her glory."

FEAST DAY AUGUST 15th

The Assumption of our Lady represents the happy departure of Mary from this life to be reunited with her son. God honoured Our Lady by taking her whiole body into heaven at her death, the only fully human soul to be united with the body after death before the judgement at the end of time. 
The Blessed Virgin Mary went from the divine life of being Mother of Jesus to be exalted forever in the life to come as the Queen of Mercy and Compassion. 
This feast reminds us of eternity and gives us hope that we, too, will follow Our Lady when our life is ended. It also tells of Gods faithfullness in his infinite love for her, and through her and her son, for us also.
Even though there is no hard historical evidence of the Assumption, this Feast has been celebrated for centuries, becoming dogma in 1950 as declared by Pope Pius 12 that the event was revealed by God.. This lack of historical evidence has created opposition to this event which must also question infallible declaration of the Pope. 
Our Holy Father Pope Benedict 16's view is clear (as cited http://www.deism.com/to-natures-god.net/page_67.htm )
As you say, Pope Pius 12 declared Mary's Assumption a dogma of the Church in 1950. The truth of this event did not depend on the Bible nor on the early tradition of the Church. It simply needed the infallible declaration of Pope Pius 12. When that happened, I no longer had any reason to doubt Mary's Assumption.