"Mary set out and went as quickly as she could into the hill country to a town in Judah. She went into Zachariah's house and greeted Elizabeth."
Luke 1:39, 40

The Visitation is such a simple event: one woman goes to visit another. And yet Luke recounts it in the first chapter of his gospel because that simple fact carries profound meaning. That meaning was once described as follows:

because a woman came who carried Christ within her,
there was a change in someone else.

Mary had just said yes to God's presence within her, and so when she visited Elizabeth, God visited Elizabeth as well, enlivening the baby in her womb.