For many, The Magnificat is a lovely response by Mary to her cousin Elizabeth when she said "And why is this granted me, that the mother of my Lord should come to me?" (Luke 1:43). But it is so much more!
There are those that consider Mary to be a "simple" Jewish girl caught up in the wonderful tales of the Bible. The Magnificat in a lot of ways shows that Mary is a well schooled, faithful child of Israel. The Magnificat mirrors the Song of Hannah in thanks for the birth of her son Samuel (1 Sam 2:1-10) as she believed herself barren.
As Tom discusses, in the Magnificat, Mary fully embraces the divine grace and offers thanksgiving from the soul.
On a side note, there are also many who say that the line "and my spirit rejoices in God my Saviour" suggests that Mary needed a saviour and therefore could not possibly be free from sin. This again goes to show the awesome power and the nature of the Divine Plan, as well as the significance of Our Blessed Mother that God chose to pre-emptively save her from before her conception. This is what Vatican II had to say:
"The Father of mercies willed that the incarnation should be preceded by the acceptance of her who was predestined to be the mother of His Son, so that just as a woman contributed to death, so also a woman should contribute to life. That is true in outstanding fashion of the mother of Jesus, who gave to the world Him who is Life itself and who renews all things, and who was enriched by God with the gifts which befit such a role. It is no wonder therefore that the usage prevailed among the Fathers whereby they called the mother of God entirely holy and free from all stain of sin, as though fashioned by the Holy Spirit and formed as a new creature" (Lumen Gentium 56)