Why would Luke highlight the meeting between Mary and pregnant Elizabeth? He could have simply stated that Mary hurriedly visited and stayed with Elizabeth for about three months. Yet, he does not. He considers their meeting important enough to use up precious space in his narrative (a scroll) to record their meeting and greeting one another. What does all this mean for believers both in the first century AD and today?
First of all, we must understand that Mary’s greeting (Luke 1:40) wasn’t a simple “Hello!” Eastern culture demanded much more than that and took quite a long time by today’s standards. Rather, salutations in the Eastern culture were expressed with several embraces and bowing, even lying prostrate with one’s face to the ground was not uncommon (cf. Genesis 33:1-7). While she greeted Elizabeth, we should not expect that Mary was silent about the reason for her visit. No doubt she spoke of Gabriel’s words, including his telling her of Elizabeth’s pregnancy, which was to be a sign to Mary that she would bear the Messiah.
We often hear it taught that, because Elizabeth was filled with the Holy Spirit as soon as Mary began to greet her (Luke 1:41), God revealed to Elizabeth that Mary was pregnant with the Messiah. However, this doesn’t take into consideration that the scripture says Elizabeth was filled with the Holy Spirit after Mary was finished saluting her. That is, Elizabeth wasn’t filled until Mary was finished speaking. What did Mary say in her salutation? I can think of nothing except to tell Elizabeth the reason for her visit—i.e. the angel telling Mary what would occur to her and that Elizabeth was in her sixth month of pregnancy.
If we are to understand what Luke means by recording this meeting, we need to keep in mind that, although John was filled with the Holy Spirit from birth, yet he did not know that Jesus was the Messiah, until God showed him a sign (John 1:31-33). If John, who was filled with the Holy Spirit from birth until death and didn’t know Jesus was the Messiah without a sign from heaven, how did Elizabeth know Mary was the mother of the Messiah, unless a sign was in Mary’s greeting, about which the Holy Spirit inspired Elizabeth to believe and comment on with encouragement? We must not try to ascribe to Elizabeth what the scriptures fail to attribute to John, of whom Jesus testifies there was no greater prophet in all Israel (Matthew 11:11; Luke 7:28).
What meaning, therefore, lies behind this meeting? I suggest that it has to do with the ending of an era and the beginning of another. John represented the Old Covenant, but Jesus and the New Covenant were far superior. Notice in Luke 7:28, mentioned above, that the prophet John is placed in contrast to those in the Kingdom of God. When John understood that Jesus was the Messiah, he wanted Jesus to take over his ministry, and he (John) would serve him (Matthew 3:13-17), but Jesus denied his request, saying their ministries must be separate. The Law and the Prophets were until John, but, since the time of John, the Kingdom of God is preached (Luke 16:16).
Only Elizabeth’s greeting to Mary is recorded by Luke (Luke 1:41-45), but notice what she says. The babe leaped in Elizabeth’s womb after Mary was finished greeting Elizabeth (Luke 1:41, 44). She told Mary she was blessed among all women for the service she was called to perform, and the child that would be born of her was blessed (Luke 1:42). Moreover, Elizabeth considered it a great, undeserved honor that the mother of the Messiah would visit her (Luke 1:43; cf. 2Samuel 24:21), again pointing to the superior ministry of Jesus.
Finally, Elizabeth blessed Mary for believing the angel, declaring out of her own experience that the Lord would, indeed, perform all that was told to her (Luke 1:45), which calls into question when Mary conceived. Did she conceive immediately after Gabriel’s visit, or did she conceive when she was assured in seeing Elizabeth that the angel’s words could be believed? I hold to the latter.
 Luke’s Gospel scroll comes to about 32 feet in length. “Luke–Acts may be closer to standard forms of Greco-Roman historical writing than are the other Gospels, which resemble ancient biography. Whereas Matthew, Mark and John wrote forms of ancient biography, Luke’s second volume shows that he wrote history as well. Luke and Acts are each roughly the same length as Matthew, with Mark one-half and John two-thirds that length, indicating scrolls of standardized lengths (Matthew, Luke and Acts were each close to the maximum length for scrolls, between thirty-two and thirty-five feet). “ [Keener, C. S., & InterVarsity Press. (1993). The IVP Bible background commentary : New Testament . Downers Grove, Ill.: InterVarsity Press.]
 See Barnes’ Notes on the Bible at Luke 10:4