Nobody knows the true date of Jesus' birth! This date is not specified in the Bible, so why are we celebrating His birth 25 of December? Likewise, Jesus' birth probably did not happen in A.D.. A.D., but a bit earlier. Somewhere between 2BC and 7BC (before Christ).
The first recorded Christmas celebrations took place 25 December 336. in the time of the Roman emperor Constantine (he was the first Christian Roman emperor). A few years later, Pope Julius I officially declared, that the birth of Jesus would be celebrated 25 of December.
There are many different explanatory theories, why is christmas celebrated 25 of December. Earlier in the Christian tradition it was adopted, that 25 March was the day, in which Mary said, that she would give birth to a son Jesus. (Annunciation). Nine months after 25 March is 25 of December.
Christmas was also celebrated by the early Church on 6 January, when today is the Feast of the Epiphany and the Baptism of Jesus. Jesus' baptism was initially viewed as more important than his birth.