He was born at the end of September, around Michaelmas Day, and just to make it easier for people to catch onto Christianity, switching from paganism which had celebrations around what we know now as Christmas time. As far as the bible is concerned, its not a big issue about what day in the year he was born incarnate.
Also, switching it to the winter solstace paralleled what Christianity was about, joy to all, even in the darkest of times, and renewal, as the days get longer and longer, and Jesus was about overcoming darkness and achieving resurrection to everlasting life.
There's no evidence that Jesus was born on Christmas. The Romans were trying to win over more converts and assigned the date to coincide with their popular festival, Saturnalia. Gift giving was a big part of Saturnalia, so it just sort of got absorbed into the "Christian" tradition.
He wasn't born on Christmas (Dec 25th)...
He was born earlier (maybe in the spring time)...
The church moved the birthday because of the winter solstice.
Ok, folks...the gifts have nothing to do with christianity at all. In fact, America is largely responsible for popularizing gift giving at christmas (although this started as a Dutch tradition) turning it into the holiday marred by capitalism that we know today.