FSogol's Advent Calendar Day 21: Origin of The Yule Log
Origins: Though few Americans still bother with it, the burning of the yule log was at one time one of the most firmly entrenched customs of Christmas. Everything to do with them was fraught with ritual certain formulas had to be followed very carefully lest disaster befall the household in the upcoming year. It was unlucky to buy a yule log. Lucky ones were obtained from ones own land or from a neighbors wood. Often a stump or a root (not necessarily a proper log at all), it was brought home on Christmas Eve and laid in the hearth.
The first step towards lighting the yule log was fetching the carefully-preserved scrap of the previous years log from under the homeowners bed. Having done its job of keeping the house safe from fire and lightning since the last festive season, it was now used to light the new log. The new log had to catch fire during the first attempt at lighting it; its failure to do so was a sign of misfortune coming to the family. Such an important duty had to be handled gravely. And clean hands only, please to attempt to light the log with dirty hands would have been an unforgiveable sign of disrespect.
Once lit, the log had to be kept burning for twelve hours. This was not always an easy task, as special caution was given against stirring the embers during the lengthy Christmas Eve supper. The log could not be tended as long as any scrap of the dinner remained on the table, or while anyone was still eating. As the log burned, people told ghost stories and tales of olden times whilst drinking cider. Shadows cast upon the wall were carefully scrutinized, for it was well known that a headless shadow foretold the death of the person casting it within the year.
In later years and in more urban settings, a Christmas Candle was substituted and followed the same tradisitons. A bit of the candle was saved for the next year.
A much more popular version of the yule log is available to modern society the buche de noel. Rolled, frosted in chocolate, and decorated to look like a yule log, this sponge cake is served as part of the Christmas Eve meal in France called reveillon, which takes place after midnight Mass.
From Snopes:
https://www.snopes.com/holidays/christmas/yulelog.asp
Edited to add this is another Christmas tradition that made its way over from Norse mythology. They were originally burned as a prayer to Odin to keep the house safe from lightening and fire thru the year. Odin traveled around the world (sound familiar?) each night and the log was burned on Dec 25 which the Norse, most Germanic peoples, the Celts, and the Romans believed was the Winter Solstice and end of the year.