With regard to the solemnity of the Nativity of John the Baptist and the Gospel passage that focuses directly on that event: The birth itself is stated without any details. More time is spent describing the circumcision and naming of this newborn child. And finally the response of the neighbors is given. They are not sure what to make of this child or what he was destined to become.
1) The birth of John the Baptist. Luke offers only a bare-bones statement indicating that Elizabeth gave birth to a son. Previous to this Zechariah was visited by the archangel Gabriel who announced that this was going to happen even though Elizabeth was elderly and barren (Lk 1:5-25). This is the fulfillment of that prophesy and the neighbors all rejoice with Elizabeth.
2) Circumcision and naming of the child. Eight days after the birth of this child he is presented for circumcision and at this time he will receive his name. Circumcision officially incorporates John the Baptist into the people of Israel. He is now part of the covenant people. Ordinarily he would have received the name of his grandfather, or on occasion the father's name is given a newborn child. Elizabeth is the one who first declares that this child will be named “John.” This was previously mandated by the angel Gabriel but he told it only to Zechariah (Lk 1:13). Nevertheless, this name totally shocks everyone who heard it. Zechariah himself is then consulted and he confirms what Elizabeth had declared, “John is his name.” It is quite clear from what has already taken place that this child's ultimate mission will be anything but normal.
3) The neighbor's response. Zechariah recovers his voice which was taken from him by the archangel Gabriel. His first words express blessings on God. The neighbors, on the other hand, experience the kind of fear that emerges from being in the presence divine mystery. From annunciation to birth the events surrounding John the Baptist have been extraordinary. Who is this child and what is he destined to become? He was born to pious faithful Jews who were just ordinary folks. But obviously out of the ordinary is going to emerge the extraordinary. In the meantime he will be in the desert growing strong in spirit.