In the western world the birthday of Jesus Christ has been celebrated on December 25th since AD 354, partly to replace the pagan worship that was commonplace in those days. However, we can be fairly sure that Jesus wasn't actually born on that date. (See also The History of Christmas)
The Bible tells us that shepherds were staying out in the fields overnight when Jesus was born (Luke 2:8), but in that part of the world it would have been far too cold at night to do so in December. What is more likely is that He was born in the Spring, perhaps between March and May. Whatever the time of year, it is virtually impossible to identify the actual date.
This situation is further complicated by the fact that the Christian scholar Dionysius Exiguus was asked by the Pope in AD 525 to calculate new cycles for fixing the date of Easter. However, he decided to base his calculations on the date of Jesus's birth. Unfortunately, it wasn't discovered until the 9th century that he got it badly wrong, by which time it was too late to change the calendar.
He fixed the birth in the year 1 BC or AD 1 (Historians apparently can't agree which.) and began counting from the latter. But both earlier and later scholars agreed that Jesus was born at an earlier date. Indeed, it was eventually established that Herod the Great died in Spring of 4 BC. If Jesus had been born at the start of AD 1, as we currently have it, then Jesus would have been born some 4 or 5 years after Herod died. There is no way of accurately establishing the actual date of his birth, but it is most likely to have been between 5 and 6 BC..
The important thing is that he was born, and his nominal birth date of December 25th seems as good as any to celebrate his birth and his message. It also a wonderful catalyst for enjoying the precious and simple pleasures of being, if only for a brief time, close together in the warm familiarity of friends and family, renewing relationships and sharing memories.