According to Luke: An Analytical Commentary

Luke 1:10-13

10 And the whole multitude (a large crowd of worshippers) of the people (Israelites gathered for public prayer) were praying without (outside the Holy Place; in the court) at the time of incense (incense offering was linked with prayer; cf. Psalm 141:2).

11 And there appeared (became visible; sudden manifestation) unto him (Zacharias personally) an angel of the Lord (messenger sent from God; this is the first time Zacharias ever saw an angelic being) standing on the right side (position of favor and authority) of the altar of incense (the small golden altar before the veil).

12 And when Zacharias saw him (the angel/messanger), he was troubled (deeply agitated; fear and awe common in angelic encounters), and fear fell upon him (overwhelming terror).

13 But the angel said unto him, Fear not, Zacharias (command to not be afraid, reassurance; named personally), for thy prayer is heard (God has answered his long-standing prayer for a child), and thy wife Elisabeth (specific personal reference) shall bear thee a son (promise of miraculous conception despite age), and thou shalt call his name John (Meaning: “Jehovah is gracious”, named by God).