Saint Elizabeth's name in Hebrew is אֱלִישֶׁבַע / אֱלִישָׁבַע or "My God has Sworn". In the Gospel of Luke, we learn she was one of the daughters of Aaron and her and her husband were "Righteous before God". At the age of nearly 60, she was well past child bearing age. The following verses in the Gospel of Luke tell of when her husband, Saint Zechariah went to pray at the temple and was visited by the Angel Gabriel:
10 And when the time for the burning of incense came, all the assembled worshipers were praying outside.
11 Then an angel of the Lord appeared to him, standing at the right side of the altar of incense. 12 When Zechariah saw him, he was startled and was gripped with fear. 13 But the angel said to him: “Do not be afraid, Zechariah; your prayer has been heard. Your wife Elizabeth will bear you a son, and you are to call him John.
14 He will be a joy and delight to you, and many will rejoice because of his birth,
15 for he will be great in the sight of the Lord. He is never to take wine or other fermented drink, and he will be filled with the Holy Spirit even before he is born.
16 He will bring back many of the people of Israel to the Lord their God.
17 And he will go on before the Lord, in the spirit and power of Elijah, to turn the hearts of the parents to their children and the disobedient to the wisdom of the righteous—to make ready a people prepared for the Lord.”
18 Zechariah asked the angel, “How can I be sure of this? I am an old man and my wife is well along in years.”
19 The angel said to him, “I am Gabriel. I stand in the presence of God, and I have been sent to speak to you and to tell you this good news. 20 And now you will be silent and not able to speak until the day this happens, because you did not believe my words, which will come true at their appointed time.”
21 Meanwhile, the people were waiting for Zechariah and wondering why he stayed so long in the temple.
22 When he came out, he could not speak to them. They realized he had seen a vision in the temple, for he kept making signs to them but remained unable to speak.
23 When his time of service was completed, he returned home.
For the next six months, Saint Elizabeth, now pregnant remained in seclusion. Immediately after the Virgin Mary received the words from the Angel Gabriel that she would conceive Jesus, Mary left and went to visit Elizabeth in Hebron.
After this his wife Elizabeth became pregnant and for five months remained in seclusion. “The Lord has done this for me,” she said. “In these days he has shown his favor and taken away my disgrace among the people.”
39 At that time Mary got ready and hurried to a town in the hill country of Judea,40 where she entered Zechariah’s home and greeted Elizabeth.
When Elizabeth heard Mary's greeting, the baby in her womb "leaped" with Joy:
When Elizabeth heard Mary’s greeting, the baby leaped in her womb, and Elizabeth was filled with the Holy Spirit. In a loud voice she exclaimed: “Blessed are you among women, and blessed is the child you will bear! But why am I so favored, that the mother of my Lord should come to me? As soon as the sound of your greeting reached my ears, the baby in my womb leaped for joy. Blessed is she who has believed that the Lord would fulfill his promises to her!”
— Luke 1:41–45
Mary stayed with Elizabeth for about three months and then returned home. When it was time for Elizabeth to have her baby, she gave birth to a son. Her neighbors and relatives heard that the Lord had shown her great mercy, and they shared her joy. On the eighth day they came to circumcise the child, and they were going to name him after his father Zechariah, but his mother spoke up and said, “No! He is to be called John.” They said to her, “There is no one among your relatives who has that name.” Then they made signs to his father, to find out what he would like to name the child. He asked for a writing tablet, and to everyone’s astonishment he wrote, “His name is John.” Immediately his mouth was opened and his tongue set free, and he began to speak, praising God.
— Luke 1:56–64
Saint Elizabeth is revered as a Saint and celebrated on November 5th in the Roman Catholic Church, with the Orthodox and Anglican churches celebrating her on September 5th.