The birth of John the Baptist marked the Church Age, when God showed grace after a period of silence for 200 years.
What do I mean by this? This insight comes from the Hebrew name of John, יוֹחָנָן (translated into koine Greek as Ἰωάννης) which means,
"He (God) shows grace."
The root word is the verb חָנַן (refer to Genesis 33:5) which means:
חָנַ֥ן (חנן) חנן־1 Verb qal perfect 3 masculine singular meaning 'to show favor'
[ESVS] H2603 given
After bringing the nation back from the exile, God was disappointed with the people; ֶHe sent one prophet after another, but the people of Israel did not heed the words of the Prophet.
Hence, we have a period of silence for the next 200 years.
Just before Christ was born, John the Baptist was born. It was the angel Gabriel who announced the name to Zechariah.
The name was the beginning of a new era where God would show His grace towards mankind. The body of Christ is the bearer of the good news of God's grace. Let us share this with all our loved ones.