The birth and circumcision of John the Baptist are here described. (Earlier in the chapter we see the significance of John’s conception, re: Zacharias and Elizabeth, 5-23).
The Lord’s blessing upon Elizabeth was a cause for great joy to her neighbors and relatives, who rejoiced with her (58).
It was required of the Jews by law to circumcise male children on the eighth day following birth. At this time they named him John. John was not a family name, so it had to be confirmed by both Elizabeth and Zacharias his name would be John, as directed by the Lord in a vision to Zacharias in 1:13.
At this time, the Lord also loosed the mouth of Zacharias (he had been mute since the vision of 1:5-23. However, though God had indicated to Zacharias the nature of the boy, it was not yet known to the friends and relatives, who rejoiced at the miracle of the return of Zacharias’ voice, and asked in wonder, “What kind of child will this be?” One who would be a great servant of God!