The Gregorian calendar, which was introduced in 1582 AD by Pope Gregory XIII, is a revision of the Julian calendar.  The Gregorian calendar is also known as the Christian calendar because it uses the birth of Christ Jesus as a starting date (December 25th, 1BC.)  Due to calendar chronology problems, however, most biblical scholars place the date of the birth of Christ Jesus as early as 7BC, and no later than 4BC.

The Bible tells us that Quirinius (Cyrenius) was the Roman governor of Syria when a decree went out from Caesar Augustus (the Roman Emperor) ordering a census to be taken of all the provinces ruled by Rome for taxation purposes.  It was during this time that Christ Jesus was born in Bethlehem.¹

As to this time, the Liberty Bible Commentary reminds us that Syria was the most important of all the Roman provinces, and Quirinius (Cyrenius) served in several capacities there at different times.  It also reminds us that Roman censuses came every fourteen years (the first that was recorded was in 6AD.)  This earlier census (the one taken during the birth of Christ Jesus) may have been set in motion, by Rome, as early as 8BC, while Quirinius was the military governor of Syria.  Several years would have been required to complete such a census.

Bible References:

¹ (Luke 2:1-7)