Since becoming Catholic I have understood this on an intellectual level, but I did not begin to understand it on an spiritual level until I began attending daily mass; and this article from Pope Benedict, which is serving as the introduction to the first volume in the multi-volume edition of his writings, is a focus on that.
An excerpt.
“Ever since my childhood, the Church's liturgy has been the central activity of my life, and it also became, under the theological instruction of masters like Schmaus, Söhngen, Pascher, and Guardini, the center of my theological work. I chose fundamental theology as my specific topic, because I wanted above all to go to the heart of the question: why do we believe? But right from the beginning, this question included the other one about the proper response to to God, and therefore also the question about the divine service. It is on this basis that my work on the liturgy must be understood. I was not interested in the specific problems of liturgical study, but in the anchoring of the liturgy in the fundamental act of our faith, and therefore also its place in our entire human existence.
“This volume now collects all of my short and medium-length work in which over the years, on various occasions and from different perspectives, I have expressed positions on liturgical questions. After all of the contributions that came into being in this way, I was finally prompted to present a vision of the whole, which appeared in the jubilee year 2000 under the title "The Spirit of the Liturgy." This constitutes the central text of the book.
“Unfortunately, almost all of the reviews of this have been directed at a single chapter: "The altar and the direction of liturgical prayer." Readers of these reviews must have received the impression that the entire work dealt only with the orientation of the celebration, and that its contents could be reduced to the desire to reintroduce the celebration of the Mass "with [the priest's] back turned to the people." In consideration of this misrepresentation, I thought for a moment about eliminating the chapter (just nine pages out of two hundred) in order to bring the discussion back to the real issue that interested me, and continues to interest me, in the book. It would have been much easier to do this because in the meantime, two excellent works had been published in which the question of the orientation of prayer in the Church during the first millennium is clarified in a persuasive manner. I think first of all of the important, brief book by Uwe Michael Lang "Turning Towards the Lord: Orientation in Liturgical Prayer" (Ignatius Press, San Francisco, 2004), and in a special way of the tremendous contribution by Stefan Heid, "Atteggiamento ed orientamento della preghiera nella prima epoca cristiana [Attitude and orientation of prayer in the early Christian era]" (in "Rivista d’Archeologia Cristiana" 72, 2006), in which the sources and bibliography on this question have been extensively illustrated and updated.
“The result is entirely clear: the idea that the priest and people should look at each other in prayer emerged only in modern Christianity, and is completely foreign to ancient Christianity. Priest and people certainly do not pray to each other, but to the same Lord. So in prayer, they look in the same direction: either toward the East as the cosmic symbol of the Lord who is to come, or, where this is not possible, toward an image of Christ in the apse, toward a cross, or simply toward the sky, as the Lord did in his priestly prayer the evening before his Passion (John 17:1). Fortunately, the proposal that I made at the end of the chapter in question in my book is making headway: not to proceed with new transformations, but simply to place the cross at the center of the altar, so that both priest and faithful can look at it, in order to allow themselves to be drawn toward the Lord to whom all are praying together.”