Because of the Bible's overwhelming dominance in Western culture, and the ubiquity of the story of Jesus, it can be difficult to separate the actual text from its many interpretations. Even for those who read the Bible regularly, it's likely they're even more familiar with the retold and passed-along versions than the words themselves.
There's no problem with this, per se, but it does mean certain misinterpretations, interpolations, and outright falsehoods tend to circulate unchallenged and become a part of the story of Jesus, despite their absence from the Bible itself. These additions can be valuable because they teach us about how our perceptions have changed over time. For example, the fact that Jesus is often believed to have white skin is an artifact from the art of the Italian Renaissance.
While many of these additions seem to be benign historical accidents, none of them happened without a reason. The idea that Jesus was born on December 25 is nowhere in the Bible. Christmas was placed on the 25th to coincide with various pagan winter festivals, absorbing them and aiding in the spread of Christianity across Europe. It's important to understand these things in order to get a full picture of how Christianity took over vast portions of the globe and came to influence the world we live in today.
This is one of those inaccuracies that is simply an addition to the story. None of the Gospel writers record December 25 as the date of Christ's birth; in fact, none of them record a date at all. There is no indication Jesus was born in the winter, spring, summer, or fall. So why December 25?
For the first three centuries after the passing of Jesus, there was no such thing as Christmas. Christians celebrated a few religious feasts, such as Epiphany and Easter, but there is no mention of Christmas on a Roman calendar until 336 CE. December 25 was likely chosen to coincide with the Roman Saturnalia festival, to make the new religion more palatable to the Romans. Indeed, one of the great strengths of early Christianity was its willingness to remake itself in the image of local religions, allowing various peoples to convert more easily.
The Three Wise Men, or the Three Kings, have become a major part of the Nativity. We see them every Christmas in window displays and Nativity pageants, but little of what we know about them is from the Bible.
Matthew 2:1 says: "Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem...", but that's all we get by way of description. Scholars have often assumed there were three of them because Jesus receives three gifts, but the Bible doesn't say for sure. There may have been dozens, there may have been two. In addition, the idea that they were kings is a later addition. There's no evidence they followed a star, and absolutely zero indication they rode camels.
Despite these additions, surely the wise men at least visited the newborn baby in a manger? Maybe not. Matthew tells us the wise men went "into the house" to meet Jesus. Not only that, the text says they came to meet "a young child." This would seem to indicate the visitation did not take place on the night of Jesus's birth, and that Jesus may have been several years old by the time he received those gifts.
St. Augustine is responsible for this idea. The great theologian - who came up with the idea of original sin - determined that original sin was passed on through the act of intercourse to the newborn. Therefore, in order for Jesus to have been born pure, Mary must have been a virgin at the time of birth. This idea has become a cornerstone of many Christian sects.
There is little mention of this in the Bible. Paul never talks about it, and most of the Gospel writers entirely skip over it. The Gospels that do talk about it, Matthew and Luke, were written a century after Jesus's end, and draw heavily from similar accounts of holy conception in the Old Testament. Indeed, the idea of the virgin birth is part of a tradition of sanctifying Mary over time to increasingly great degrees. First, she gives birth as a virgin; then, she herself was born sinless; then, she is assumed into heaven rather than passing.
The Bible clearly identifies James as the brother of Jesus and indicates Jesus had other siblings as well. So why does the Catholic Church maintain that Jesus had no siblings and lived as an only child? It has to do with what is called the Doctrine of Perpetual Virginity, which states that the Virgin Mary remained a sinless virgin to the end of her days.
Many Church thinkers have tried to resolve this contradiction, with the major response being that James must have been Jesus's cousin.