In the Western Church, we celebrate the birth of Jesus on 25th December. We don't actually know when Jesus was born. The Hebrew people and the Greeks who made up the early Christian church didn't celebrate birthdays. That was a Roman habit. When the Christian Church became the State religion of the Roman Empire, since Jesus didn't have a birthday, he had to be allocated one.
In the early Church, there was no Christmas. The start of Jesus's ministry was celebrated with a feast day on what we now call 6th January. The celebrations were focussed on the baptism of Jesus by John the Baptist. It's unclear why this day was chosen, but it seems to have been celebrated from the earliest days of the Church. Possibly it's the anniversary of Jesus's baptism. Over a couple of hundred years, the emphasis changed from Jesus's baptism to the story of his birth as given in Matthew's Gospel. (No manger, no shepherds, but wise men - not necessarily 3 - with gold frankincense and myrrh). The baptism celebration was moved to the following Sunday.
When Paul established the Church in Ephesus, there was already an established fertility cult based upon the temple of Artemis, a manifestation of the Greek goddess Diana. Their main celebration was at the vernal equinox - 24th March in the Julian calendar. Paul replaced it with the feast of the Annunciation, later recorded in Luke's Gospel, where Mary became pregnant by divine intervention.
When the Roman Emperor Constantine (born in York - that explains a lot) adopted Christianity as the State Religion, there were a couple of winter celebrations that needed to be replaced. Saturnalia was the feast where you ate and drank too much on 17th December, and the winter solstice on 24th December was the birthday of Sol Invicta, the sun god. So Jesus was allocated a birthday on 25th December (a day later than Sol to avoid confusion) 9 months and a day after his conception. This was based upon Luke's gospel (manger and shepherds, but no stable - that's a far more recent addition). The 6th January celebration continued to be marked with a bit of semantic juggling to get the two very different accounts of Jesus's birth to tally. That gave the Roman Empire 12 days off each winter.
The Orthodox, Armenian, Ethiopian, Coptic and Eastern Uniate Churches do not celebrate Christmas on 25th December. They stick to the 6th January feast.