Division of Abijah

Who was “Herod, the king of Judea” (Luke 1:5)?
See King Herod.

What is meant by Elizabeth being “of the daughters of Aaron” (Luke 1:5)?
She was a descendant of Aaron, who was the brother of Moses and whom God appointed to serve the first priest of the Jews.

What is meant by Zacharias being “of the division of Abijah” (Luke 1:5)?
Aaron had four sons. Two of them died without having children but the other two produced many descendants. After crowning Solomon as his heir, King David chose 24 male descendants of Aaron to lead 24 “divisions” - i.e., clans - of priests to perform priestly duties, including the animal sacrifices, at the tabernacle of the LORD, and then at the temple of Jerusalem to be built by Solomon. In first century AD, the 24 divisions lived throughout Israel but came to Jerusalem and served as priests during the three major feasts (Passover, Pentecost and Tabernacles) when the city filled with pilgrims and the number of animal sacrifices soared. In between these feasts, the 24 divisions took turns, always in the same order, to return to Jerusalem once about every 6 months to serve as priests for one week, starting and ending on the Sabbath day (the departing division performed the morning sacrifices from 9 AM to noon, and the arriving division performed the afternoon sacrifices from noon to 3 PM). The division of Abijah was the “eighth” (1 Chronicles 24:10) of the 24 divisions, and the rotation began at the conclusion of the Feast of Passover. Since Passover falls in April or late March in our Gregorian calendar and Pentecost falls seven weeks thereafter, the two non-feast weeks of priestly duty for the division of Abijah were in June/July and 25 weeks later (24 week + Feast of Tabernacles) in December/January; this is important to timing the birth of Jesus (see Shepherds in the Field). Both Elizabeth and Zacharias were descendants of Aaron and members of Israel's priestly clan.