“Do not be afraid, Zechariah.” This is a consistent message from God to people, and often when angels appear people are frightened and the angel then says not to be afraid (cp. Judg. 6:23; Luke 1:30). Fear is self-centered and keeps people from being all they can be for the Lord.
“your prayer.” What the angel said borders on the ironic. “Prayer” is singular in the Greek, but certainly Zechariah and Elizabeth had prayed many prayers for Elizabeth to have a child, in fact it is quite certain that prayer to have a baby would have been a high priority for them in the years past. But the angel lumps all those prayers together and refers to them as a “prayer,” focusing on the singularity of their desire and request.
The irony is that by this time, because of their old age, it is quite certain that Elizabeth and Zechariah had stopped praying for a child. In fact, it was due to their old age that Zechariah asked the angel for a sign that they would even have a child (Luke 1:7, 18). Zechariah would not have asked for such a sign if Elizabeth was of childbearing age. Thus, as Sarah at age 90 continued the genealogy to Christ by the miracle birth of Isaac, now Elizabeth would bear the forerunner of the Messiah by a miracle birth.
This record in Luke shows us that there are righteous prayers that remain alive in the mind of God and have an effect years after they are spoken. So it was that years after Elizabeth and Zechariah fervently prayed for a child, those prayers were answered. This record about Zechariah and Elizabeth is one of many miracles associated with the birth of the Messiah, and one of the many records that speak of the importance and effectiveness of prayer.
“John.” The name means, “Yahweh is gracious.”