What does it mean that the Virgin was assumed "in body" in Heaven? ... the Pope explained that the text from the Revelation, which speaks of a woman clothed with the sun, with the moon at her feet and a garland of twelve stars upon her head, refers both to the Virgin and to the Church. In part, &quot;the woman of the Apocalypse is Mary ... the symbol of the luminous robe clearly expressed a condition referring to Mary in all her being: She is 'full of grace', filled with the love of God&quot;.
The moon beneath her feet symbolises death: &quot;Mary is fully linked to the victory of Jesus Christ, her Son, over sin and death... just as death has no power over Christ resurrected, so by the grace and singular privilege of omnipotent God, Mary overcomes death. This is made manifest in the two great mysteries of her existence: at the beginning, the conception without original sin, the mystery we celebrate today; and at the end, her assumption in body and soul in Heaven&quot;.

What it is written above is an official discourse, yet it is written that the Virgin was assumed 'in body', other than in soul, in Heaven.
Can anybody explain what 'in body' precisely mean there? Does it refer to material or human body? If so, from where does Catholic Church deduce that believing? What do other Christian denominations, especially Lutherans and Orthodoxes, say about that believing?
Thank you and peace be with you.
Yes, this refers to Mary's material, human body.  The Catholic Church teaches that Mary was assumed into heaven, body and soul.  

For an explanation of the reasons behind this teaching, you would do well to read the decree "Munificentissimus Deus" of Pope Pius XII, in which he officially defined this dogma of the assumption.  The "punch line" is "by the authority of our Lord Jesus Christ, of the Blessed Apostles Peter and Paul, and by our own authority, we pronounce, declare, and define it to be a divinely revealed dogma: that the Immaculate Mother of God, the ever Virgin Mary, having completed the course of her earthly life, was assumed body and soul into heavenly glory."  This is from section 44 of the decree, so you can see that a lot of explanation preceded it.  

The whole decree is available on the Vatican web site, at http://www.vatican.va/holy_father/pius_xii/apost_constitutions/documents/hf_p-xii_apc_19501101_munificentissimus-deus_en.html (in English).  I should probably mention explicitly that, although this decree dates from 1950, the Church celebrated the feast of the assumption for many centuries before that. As far as I know, the Eastern Orthodox churches agree with this teaching, but protestants do not.