Augustus Caesar, born Gaius Octavius, was the ruler of the Roman Empire at the births of John the Baptist and Jesus Christ. He called for a periodic census in the days when Herod the Great was the client king of the Judean Province. He served as the first full emperor of the Roman empire until his death and the ascension of his adopted son Tiberius in 14 AD.
Gaius Octavius was born in 63 BC to a wealthy plebeian family that was friends with the famous general and statesman Julius Caesar. As was common in those days in Roman tradition, Julius Caesar adopted Octavius, his grandnephew, as his son and heir. When Julius was assassinated in 44 BC, Octavius began a campaign to claim that inheritance. In 27 BC he became the first Emperor of the Roman Empire. Though Julius had ruled as "Caesar," his days had been the last of the Republic.
The careers of Herod the Great and Augustus were concurrent. In good graces with the emperor, Herod had cities built in his honor. Meanwhile, he greatly expanded the Temple for the Jews in Judea. In 6 BC, Augustus received a letter from KIng Herod stating that his (Herod's) son Antipater was plotting to kill him. Augustus advised him to do what he had to. Herod had his son executed.
In the process of maintaining order, and soliciting funds, Augustus ordered that a census and taxing of the entire Roman empire take place in the later Herod's later years. Quirinius had been put in charge of Syria. It was in these days that Jesus was born in Bethlehem, the ancestral home of the House of David, the second and greatest king of Israel.
Octavius Augustus Caesar died after 40 years in power in AD 14. He was succeeded by his adopted "son" Tiberius, who had been chosen for the role years before.