The registration, or "taxing."

In the beginning of Church History: Cyrenius (Quirinius), Governor of Syria (for the second time). The registration, or "taxing." Acts 5:37. Revolt of "Judas of Galilee." Coponius Procurator of Judaea.
Cyrenius, or Quirinius, was not governor of Syria until twelve or fifteen years after the birth of Jesus. Jesus was born during the reign of Herod. At that time Varus was president of Syria. Herod was succeeded by Archelaus, who reigned eight or nine years; and after he was removed, Judea was annexed to the province of Syria, and Cyrenius was sent as the governor (Josephus, Antiquities, book xvii. chapter 5). "This was the first census of Cyrenius, governor of Syria." It is called the first to distinguish it from one afterward taken by Cyrenius, Acts 5:37. It is said to be the census taken by Cyrenius, governor of Syria; not that he was then governor, but that it was taken by him who was afterward familiarly known as governor. Cyrenius, governor of Syria, was the name by which the man was known when Luke wrote his gospel, and it was not improper to say that the taxing was made by Cyrenius, the governor of Syria, though he might not have been actually governor for many years afterward. Thus Herodian says that "to Marcus the emperor were born several daughters and two sons," though several of those children were born to him before he was emperor. Thus it is not improper to say that General Washington saved Braddock's army, or was engaged in the old French war, though he was not actually made general till many years afterward. According to this Augustus sent Cyrenius, an active, enterprising man, to take the census. At that time he was a Roman senator. Afterward he was made governor of the same country, and received the title which Luke gives him.2
Acts 5:37 After this man rose up Judas of Galilee in the days of the census, and drew away many people after him: he also perished; and all, even as many as obeyed him, were dispersed.
Judas of Galilee. Josephus has given an account of this man, (Antiquities book.17. chapter 10.5,) and calls him a Galilean. He afterwards calls him a Gualonite, and says he was of the city of Gamala, (Antiquities book 18, chapter 1.1.) In this place, he says that the revolt took place under Cyrenius, a Roman senator, who came into "Syria to be judge of that nation, and to take account of their substance." "Moreover," says he, "Cyrenius came himself into Judea, which was now added to the province of Syria, to take an account of their substance, and to dispose of Archelaus's money." "Yet Judas taking with him Saddouk, a Pharisee, became zealous to draw them to a revolt, who both said that this taxation was no better than an introduction to slavery, and exhorted the nation to assert their liberty," etc. This revolt, he says, was the commencement of the series of revolts and calamities that terminated in the destruction of the city, temple, and nation.2
In the days of the taxing. Or, rather, the enrolling, or the census. Josephus says, it was designed to take an account of their substance. Compare
“all the world should be taxed” Luke 2:1-2.
"he also perished" Luke 13:1-2
"let them alone" Proverbs 21:30; Isaiah 8:10; Matthew 15:13