Well ms Rox has given you the urban myth, now here's some history.
Christmas was first held on December 25th in Rome, Italy, sometime around 300AD.
The claim that Romans had any sort of celebration on December 25th before Christmas started is bogus. We still have original Roman calendars (called Fasti) from that time. They show Saturnalia, a harvest festival, on December 17th which carried on for up to 6 days (never more). They show NO festival on December 25th. There was no traditional festival of the sun on December 25th, there is NO historical record of it being any pagan God's birthday. Roman pagans did NOT celebrate the winter solstice. They had a word for the dark time of year - bruma - but it wasn't a festival.
Although present giving was associated with Saturnalia, it did not become associated with Christmas until many centuries later and came via a completely different route. Saint Nicholas has always been a popular saints in Europe. He was a bishop in what is now Turkey and had a reputation for generosity; for leaving gifts anonymously for poor children. A custom arose on his feast day - December 8th - of putting out small gifts for children and pretending they had come from the Saint - Saint Nicholas, Santa Claus. In parts of Europe this custom still continues today.
After the reformation, the protestants disapproved of these sorts of customs. They did not believe in venerating Saints, they thought only God should be honoured in any way. However, children still wanted their gifts so someone in Germany (supposedly Martin Luther) decided that the gifts should come from the Christ Child (the Kristen Kinder) and be given at Christmas. This custom also continues in parts of Europe - they don't have Santa. In Britan, where we already had Father Christmas, and the USA things got a bit mixed up. Santa Claus merged with Father Christmas and moved to Christmas with the presents.
The Christmas tree is also from Germany or nearby. It appears to be a left over from medieval Christmas mystery plays some of which traced the story of salvation from Adam and Eve to the birth of Christ, Christ is the new Adam, the new Tree of Life who brings eternal life to his followers. a representation of the tree was hung with dried fruit and nuts and put up on Christmas Eve (also reckoned by some to be the feast of Adam and Eve), the fruit and nuts were given to children on Christmas Day.
So the original religious celebration of Christmas started in Rome in around 300 AD. Some of the customs (presents and tree) originated in Germany around 1600 AD, were brought to Britain in the 19th century by the Royal Family and taken to the USA by both British and German immigrants in the following years.