According to Luke: An Analytical Commentary

Luke 1:7-9

7 And they had no child (childlessness was seen as a reproach or sorrow in Israel; ex. Sarah, Rachel, Hannah), because that Elisabeth was barren (unable to conceive; emphasizing God’s miraculous work later), and they both (husband and wife) were now well stricken in years (very old; well beyond normal childbearing age; sets up for a divine intervention).

8 And it came to pass (standard biblical way to mark transition to new event; historical narrative) that while he (Zacharias) executed the priest’s office (performed his assigned priestly duties) before God (in God’s presence; service in the Temple) in the order of his course (according to the Abijah division rotation schedule; 1 Chronicles 24:10),

9 According to the custom (normal regulation) of the priest’s office (specific priestly procedures laid out in the Law), his lot was (chosen by casting lots; seen as directed by God’s providence) to burn incense (offer incense on the golden altar before the veil; symbolic of prayers rising to God; cf. Revelation 8:3-4) when he went into the temple of the Lord (the Holy Place, not the Most Holy/Holy of holies).