The winter solstice is the shortest day of the year. It usually falls about December 21st.  Since ancient times, people have celebrated the winter solstice as the "rebirth/coming of the sun," because each day after the winter solstice (until the summer solstice in June) the sun shines longer. 

In the earliest days of the Christian Church, the day Jesus was born wasn't a time of great celebration.  In fact, the Bible doesn't say exactly when Jesus was born.  Bible scholars looked at clues in the Gospels to try to figure it out, but the month and day were never really certain. 

There were many celebrations that honored the old Roman gods.  One of the largest was Saturnalia, honoring the Roman god of agriculture, which was the biggest celebration of the year.  It began about December 17th, and concluded with the "Birthday of the Unconquerable Sun" on December 25th.  When the Roman Empire adopted Christianity, there was a big effort to eliminate all the festivals associated with the pagan gods.  Celebrating Saturnalia was too popular and too big to just get rid of it.  Instead, the Roman church turned it into the celebration of the unconquerable Son of God and used December 25th to honor Jesus' birth.

 In England the Queen's official birthday is a holiday, but since 1748 it has always been celebrated in the spring, regardless of when the reigning king or queen was actually born.  So it is with the birth of Jesus.  Jesus came to live among us, and it makes sense that we should celebrate His Coming. Since we don't know for sure when Jesus was born, there is meaningful symbolism in tying the birth of God's son to the rebirth of the sun.  Since most pagan cultures considered the winter solstice an important day, as Christianity spread throughout Europe transforming that pagan holiday into Christmas helped spread the Good News in a way that ordinary people could understand.  The "who" and "why" of Christmas is much more important to our faith than an exact "when"!