Luke has told us about the birth and the circumcision of John the Baptist, and now he begins his narrative of the birth and presentation of Jesus. He spends more ink here since obviously this is his main point in the prologue of the ministry.
In those days, a decree went out from Caesar Augustus, that all the world should be enrolled [RSV Luke 2]
It’s a census. It’s known that Augustus had a census now and then to get an idea of the population in various places, however he never commanded an empire-wide census. But remember that Luke’s view is a global one, and he wants this to follow that picture. Another thing to recall is that Luke is writing many years after the death of Augustus (August 14AD -yes the month is named for him) and the other events he’s telling us about. Consider trying to recall the highlights of the years of the U.S. presidency of William Howard Taft. It gives you some idea about Luke’s story. You have some general ideas about Taft perhaps, but probably not details about him. You probably don’t recall details of his role in the “Big Burn” and the forest service in 1910. But you may have some kind of general picture, legends of Augustus, if you’re Luke. Luke wants us to understand that this is an event that has world-wide significance.