What do we Celebrate at Christmas?

Christmas is not a celebration of the Birth of Christ, but rather the coming of Christ.  They are different things.

Why don't we know when Jesus was born?  Because Jews didn't celebrate birthdays... that was a pagan thing, commonly done by those who worshipped fertility gods like Ashtoreth.  So for the first 300 years, nobody cared when Jesus was born. 

But the Bible gives us some clues as to when He was born, and if we understand our Old Testament, we can narrow it down to a single week.    You see, John 1:14 says "The word became flesh, and made his dwelling among us."  The Greek word here translated as "made his dwelling" is also used in the Greek Septuagint version of the Old Testament as "Tabernacled," and is related to the "Feast of Tabernacles."  That is, the feast prefigures the coming of the Messiah.  Paul makes reference to this in Colossians 2:16-17 when He says

"16 Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath. 17 These are a shadow of the things to come, but the substance belongs to Christ."

That is, the feasts and the festivals, the Jewish holidays, are prophetic about the ministry of Jesus. 

So Jesus was likely born during the Feast of Tabernacles, which is roughly in late September or early October. 

This conforms very well to what the Bible says regarding Jesus birth.  "There were shepherds keeping watch over their flocks by night," it says, which is something that does happen in the late fall but absolutely does not happen in late December when it's too cold.  Further, the Bible tells us that Mary and Joseph were traveling as a response to a census.  This makes sense in the late fall, but by early winter, most of the roads of ancient Judea would be completely impassable, and no governor worth his office would demand everyone in his nation travel at a time when the roads were impassible. 

When was Jesus born?  given this and other clues, we can track it to about September 29th of 4 BC. 

Christmas, then, isn't about the Birth of Christ.  That's a confusion.  Christmas is about the coming of the Messiah... that is, Christmas is about the idea that God was willing to come and die for us.  It's easy, then, to see why we get it confused with His birth, but the facts point elsewhere.  Further, most educated Christians know that Jesus was not born on December 25th.  It's possible, though, that Jesus was CONCEIVED in late December, since that is roughly 9 months before September 29th.  The Catholic Church will disagree with this, and that's OK.  It's not an important issue.