I don't know about you, but I've always been puzzled about why we sing about "the yule time" or by the mention of the "yule log". What is this mysterious "yule"?
So I did a little research. It seems to be an Old Norse word jol which entered into Old English as geol. It is pre-Christian but does not necessarily denote a pagan holiday. Rather, it refers to the midwinter season of December/January. Some etymologists have speculated that this ancient word is the origin of the word "jolly" which originally meant "pertaining to a festival".
The "yule log" was a large tree trunk that was decorated and ritually burned for warmth. In other words, it was a good reason to have a cultic campfire. It made people warm and it pleased the gods. As with most pagan customs, religious practices meant that people would benefit from the offering (roasted sacrificed meats, warmth, etc.) This log would burn for days.
When Christianity took hold in England, the term "yule" was used to denote Christmas, particularly the twelve day feast from Christmas proper (Dec 25) till Epiphany (Jan 6). So there you have it. It's kind of the "Lent" which comes from the Old English lencten. This word denoted that the days "lengthened" in other words that it was Spring.