What does Luke 1:8 mean?

Only one family line could serve as priests under the Old Testament law. These were members of the tribe of Levi, through the line of Aaron (1 Chronicles 24). Aaron's descendants were grouped into 24 "divisions," who rotated duties in the temple throughout the year. Luke is describing the situation of one such priest, Zechariah, who has been unable to have children with his wife, Elizabeth, despite being known for their God-honoring lives (Luke 1:6). As they age, hope of having children has faded (Luke 1:7). Fortunately for these two, God has a plan which involves blessing their home with a child.

Good news will come to Zechariah while his division is actively serving in the temple. The timing will be incredible, as Zechariah will encounter an angel during his assigned duties. With a relatively large number of priests, and a limited number of explicit duties, it's likely not every priest performed every function. Lots—items like dice or dominoes—were used for this very reason: as an impartial way of assigning those tasks. In fact, some scholars suggest this could have been the first time, and only time, that Zechariah had the opportunity to perform the ritual offering of incense (Luke 1:9).