"In those days a decree went out from Caesar Augustus that the whole world should be enrolled" (Lk 2:1).
In setting the birth of Jesus in a historical context, St. Luke makes a statement that the coming of God in the flesh was a historical event. It was not a myth like the pagan tales of the gods. He places Jesus under the rule of Caesar, at a particular time of a decree that had a significant effect on Joseph and Mary. Because they had to be "enrolled" for the census, they had to travel to Bethlehem, the hometown of Joseph. And Jesus was born there, of course, in fulfillment of a prophecy.
Whenever we may be tempted to think that maybe a Virgin giving birth is a bit too much to believe, or that God taking on human nature and flesh is too much to expect, we should read the beginning of Luke's Gospel. The evangelist insists that this all happened in time with historical people and real places that pilgrims can visit to this day.
In addition to the historical record of the Gospels, we have the witness of faith. Those who have been touched by Jesus can see the very real and historical effect he has had on the world. By faith and facts do we know that this "all came to pass" for our good.