And Mary rising up in those days, went into the hill country with haste into a city of Juda.  And she entered into the house of Zachary, and saluted Elizabeth.
 And it came to pass, that when Elizabeth heard the salutation of Mary, the infant leaped in her womb. And Elizabeth was filled with the Holy Ghost:  And she cried out with a loud voice, and said: Blessed art thou among women, and blessed is the fruit of thy womb.  And whence is this to me, that the mother of my Lord should come to me?  For behold as soon as the voice of thy salutation sounded in my ears, the infant in my womb leaped for joy.  And blessed art thou that hast believed, because those things shall be accomplished that were spoken to thee by the Lord.  And Mary said: My soul doth magnify the Lord.  And my spirit hath rejoiced in God my Saviour.  Because he hath regarded the humility of his handmaid; for behold from henceforth all generations shall call me blessed.  Because he that is mighty, hath done great things to me; and holy is his name.  And his mercy is from generation unto generations, to them that fear him.  He hath shewed might in 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 humble.  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.  And Mary abode with her about three months; and she returned to her own house.
Now and forever. Amen.
After the angel Gabriel announces to Mary that she will conceive He who would be called the Son of God in her womb, Mary immediately makes a trip to visit her cousin Elizabeth, whom the angel has said was already in her sixth month of pregnancy. Remember that Elizabeth is in her old age, and hadn't previously been able to bear children. She was past her child-bearing years, and was known (had a reputation) to be a barren woman. So, her cousin's pregnancy, like her own, was also miraculous.
Earlier in this chapter of Luke, we see the same angel, Gabriel, bring news to Elizabeth's husband, Zachary, that she would conceive and bear a son. He had been struck dumb and mute for his disbelief, even as he was offering up incense on the altar of sacrifice within the Temple. That happened six months prior to the scene above. Elizabeth was no doubt in a difficult position, being an elderly woman who was pregnant, and with a husband who could not speak, which would have made daily living problematic.
A visit from her younger cousin must have been a welcome blessing and help.
Elizabeth was Filled with the Holy Ghost
Upon hearing Mary's greeting, Elizabeth is filled with the Holy Spirit. This points to the Doctrine that says Mary is the Mediatrix of All Graces, which is held by the Catholic Church. This is the teaching that Mary dispenses the Graces of God according to the authority that He has bestowed upon her as Jesus' own mother.
This has a lot to do with Jesus being a king in the line of David. In the Davidic Kingdom, the Queen Mother held a high status, not the Queen. The Queen Mother had an official title, Gebirah, which means "Great Lady." The Gebirah was the most important woman in the royal court, and the king's chief advisor. Of the 20 Davidic kings after Solomon, 16 of the Gebirah were listed alongside the names of the kings.
Along with acting as chief counselor to the king, the Gebirah also acted as intercessor to the king on behalf of the people, she held royal authority in times of warfare, and she also distributed goods out of the royal treasury to the people.
In the Eternal Kingdom, the royal treasures are the graces merited by the sacrifice of Jesus on Calvary. Mary, in her position as Gebirah, dispenses these graces in union with the will of Her Son. We see that happening here, in this passage, whereby the Holy Spirit fills Elizabeth by virtue of the greeting of Mary. Mary continues even now as Gebirah, and devotions to Our Lady yield great fruit, as she intercedes for us to Jesus, and graciously gives us the graces we need to come into union, or deeper union, with Her Son.
The Mother of My Lord
Having received the gift of the Holy Spirit through the greeting of Mary, Elizabeth is inspired with the knowledge of both Mary's pregnancy, which must have only been a few days old now, and also who it is she is pregnant with. Elizabeth immediately recognizes the Divinity of Mary's Son ("Lord" is a reference word for "the Lord God"), this is very much like the inspiration that Simon Peter receives from the Father when he says "Thou art Christ, the Son of the living God" in Matthew 16:16.
And it is this fact, that Mary is the mother of God ("my Lord"), which is the reason Elizabeth can say "Blessed art thou among women, and blessed is the fruit of thy womb." Her motherhood is the source of her blessing. But, her blessing has another source: "blessed art thou that hast believed, because those things shall be accomplished that were spoken to thee by the Lord." Her belief, her "yes," her assent to the will of God is the source of her blessing. Her belief was a positive act of the will, the cooperation with the will of God, and assent to His will allows Him to accomplish His will through her, and by this she is blessed.
And it is the inspiration of the Holy Spirit that reveals this to her in such a moment of joyful reunion.
The Babe Leapt for Joy
However, even before we're told that Elizabeth was filled with the Holy Spirit, we're told first that the babe in her womb (John) leapt for joy. And then afterward, we are told Elizabeth is filled with the Holy Spirit, and in that same inspired declaration about the Divinity of Jesus, Elizabeth says that the babe in her womb leapt for joy. Remember, this is an inspired declaration, so it has import. This is not a simple movement of the child, like feeling the child kicking, which she must have felt many times before this.
There is a tradition in the Church, not an official teaching, but an old tradition that says that this was the moment that John received his mission as Baptist. Whenever we speak of Elizabeth's son, it is always with the title "the Baptist" attached. This indicates mission, in the same way that Simon is normally referred to as Simon Peter, or Mary is called Kekaritomene. The tradition holds that, upon hearing the greeting of Mary, John was baptized in Elizabeth's womb, and that, though he was not conceived without original sin, he was born without it.
So not only did Mary's greeting inspire Elizabeth to make a profession of Faith, but it also effected Sacramental Baptism upon John. This is another demonstration of the dispensational capacity of Mary as Gebirah in the Eternal Kingdom.
And Mary Said
Following these exclamations made by Elizabeth, we see Mary's Magnificat, the most amount of talk we see in Scripture from Mary. This passage gives us the most insight into the mind of Mary, and it is revealing, indeed. She first begins speaking about herself, and God's activity with her. Then makes pronouncements about the future, and then about the past.
My Soul Magnifies the Lord: Here, Mary explains her role in God's plan, and why it is that these miraculous things take place by her greeting (Inspiration and Baptism). Mary's soul magnifies the Lord. She does not take away from Him, from His majesty, goodness, mercy and love. She magnifies Him, making Him grow and take up a larger place in our lives. And this has been the consistent experience of those who carry on a devotion to Our Lady: that Jesus becomes a greater priority and focus in their lives. This is what she does.
My Spirit has Rejoiced in God my Saviour: Knowing that Jesus is our Saviour, we see here once again that Jesus is identified as God. But, Mary also identifies as someone who needs salvation, otherwise she would not call God her Saviour. This passage is often used to demonstrate that Mary was, in fact, not sinless. But, to say this is to suggest that her title, Kekaritomene, is false. But Scripture does not contradict Scripture. In order to understand that Mary was indeed in need of a Saviour, we must realize that it is by the grace of Jesus' Sacrifice that Mary was preserved from sin. In other words, she was saved "before the fact" and everyone else is saved "after the fact", but whether before or after, we all need to be saved. The work of Jesus is Eternal because He is Divine, not just human. Therefore, His graces may be dispensed during any period of time, either before or after the historical event, according to His will. This is why, for example, even though Jesus had not yet established His Kingdom within the context of history, Mary was Gebirah even at this moment, while He was yet in her womb, because His Kingdom exceeds the bounds of time.
All Generations: Mary then makes two pronouncements about the future: "all generations will call me blessed" and "his mercy is from generation to generation." The reason for both of these statements is the same: Jesus. "Because he that is mighty, hath done great things to me; and holy is his name." Jesus is the reason Mary is blessed, and by her assent to the will of God to bring Jesus into the world to accomplish His mission, we acknowledge her blessedness. And Jesus is the reason God's mercy extends from generation to generation, because His work is Holy, and is for all generations. But not for all people: only those who "fear him." Remember that.
He has Received Israel: Mary then recalls all that the Lord has done for His people, drawing our attention to the fact that this work God has worked with her, the Child in her womb, is the fulfillment of all His work throughout the Old Testament--it is the fulfillment of all His covenants. There are two virtues she highlights in particular: humility and hunger (for Righteousness). These speak to a recognition of one's own need for God (as opposed to those who are proud and think they do not need Him), and a desire to have that need fulfilled. That first, we recognize we cannot be Righteous of our own work, and second that we have this desire to be Righteous, and it is for these people, the humble and hungry, that Jesus comes. He has received Israel upon whom He may lavish His mercy, as He promised to Abraham and his descendants.
And Mary stayed with her cousin for three months before returning home. Remember, Elizabeth was already in her sixth month. In other words, Mary stayed with her cousin until John was born, at which time Zachary was healed of his dumb/muteness, and her help was no longer needed. What a thoughtful cousin. What a thoughtful mother she must also be.
Thanks for reading!