A Christmas carol is a carol whose lyrics are on the theme of Christmas, and which is traditionally sung on Christmas itself or during the surrounding holiday season. Christmas carols may be regarded as a subset of the broader category of Christmas ... music
"A yule log is a large wooden log which is burned in the hearth as a part of traditional Yule or modern Christmas celebrations in several European cultures." http://en.Wikipedia.Org/wiki/Yule_log
If you have a fire place it is an actual log where you save part of the bark for the following year and use the past years bark in its place. In my house It represents the cycle of the year.
If you dont have a fire place it is a simple log round with a candle and wreath. You light the candle each year for the same purpose.