The Magnificat is a canticle—a hymn taken from the Bible. When the angel Gabriel visited the Virgin Mary at the Annunciation, he told her that cousin Elizabeth was also with child. Mary went to see her cousin (the Visitation), and the baby in Elizabeth's womb—John the Baptist—leapt with joy when Elizabeth heard Mary's voice.
The Magnificat (Luke 1:46-55) is the Virgin Mary's response to Elizabeth's greeting, glorifying God and thanking Him for choosing her to bear His Son. It is used in the Evening Prayer of the Liturgy of the Hours, the daily prayers of the Catholic Church. We can incorporate it into our evening prayer, too.
The Annunciation and the Visitation gave us another famous Marian prayer, the Hail Mary.
My soul doth magnify the Lord:
And my spirit hath rejoiced in God my Saviour
Because He hath regarded the lowliness of His handmaid: for, behold, from henceforth all generations shall call me blessed.
For He that is mighty hath done great things to me: and holy is His Name.
And His mercy is from generation until generations, to them that fear Him.
He hath showed might with His arm: He hath scattered the proud in the conceit of their heart.
He hath put down the mighty from their seat, and hath exalted the lowly.
He hath filled the hungry with good things: and the rich he hath sent empty away.
He hath received Israel His servant, being mindful of His mercy:
As He spoke to our fathers, to Abraham and to his seed for ever.