If you are serious about wanting to know why we celebrate Christmas on Dec 25, here are some facts to ponder...
The first recorded date of Christmas being celebrated on December 25th was in 336AD, during the time of the Roman Emperor Constantine, who was the first Christian Roman Emperor. A few years later, Pope Julius I officially declared that the birth of Jesus would be celebrated on the 25th of December. As latony007 pointed out above, some say that Constantine chose that date as there was already a pagan Roman holiday that was widely celebrated around that date called "Saturnalia" (in honor of the god Saturn).
The actual birthdate of Jesus (or even the actual year) is not known, as there is no mention of it in the Bible. However, the year was probably around 5-6BC, which coincides with certain historical events mentioned in the New Testament. King Herod died in 4BC, so it had to be before then. We know that in an attempt to kill Jesus, Herod ordered all boys 2 years and younger in the vicinity of Judea to be killed. This indicates that Jesus could have been as old as 2 by the time of Herod's death. Also historical records show that the census that included Judea (that Joseph and Mary were obligated to attend) was held around 6BC. There are other historical events mentioned in the New Testament that would fall into this historical timeline as well.
Of course, as others have said, the exact date really shouldn't matter to us some 2020 years later. Folks were simply not very good time keepers back then.