In the passage we’re looking at today, Luke resumes the story of Z and E and the birth of John the Baptist that he began earlier in the chapter (cf. 1.5-25). The angel had visited Z and assured him that his wife would have a baby, even though she was an old, barren woman. Nine months has now elapsed, and E is ready to give birth; the time has come for God to fulfill his promise.
A key theme in this passage is the fulfillment of God’s promises. God said that this would happen, and it does. God’s promise came true.
The other major theme here is obedience. Z and E obey God’s command regarding their son.