Scientifically, the Winter Solstice occurs when the earth's axial tilt is farthest from the sun. For people in high latitudes, this event is commonly considered the shortest day of the year. The seasonal significance of this astronomical event is the reversal of the gradual shortening of days. A coming of brighter, longer days. Hope for the season to come.
Did you know? Apparently the tradition of the Yule tree was very common in Germany and its neighboring countries due to their shared old Nordic ancestry, but it did not cross the sea to England - and thereby to America and Australia - until around 1830 when Prince Albert went to visit Germany with Queen Victoria. He became so enamored of their yule tree custom, that he insisted they replicate the tradition at court. And from there, the fun and tree-cutting spread like (dare I say it) wildfire.
Similarly, the Yule log was burned throughout the solstice night to provide a light in the darkest night and to symbolize hope and faith that the sun will soon return. In Scandinavia, great Yule logs were burned all throught the night, and people drank mead around the bonfires listening to minstrel-poets singing ancient legends. It was believed that the Yule log had the magical effect of helping the sun to shine more brightly in the coming year.
Another Yule tradition that has carried through to modern times is mistletoe. Mistletoe was sacred in the Yule festival because it mysteriously grew on the most sacred tree, the oak. It was ceremoniously cut and a spray of it was given to each family, to be hung in the doorways as good luck. The celtic Druids also regarded mistletoe as sacred. Druid priests cut it from the tree on which it grew with a golden sickle and handed it to the people, calling it All-Heal. To hang it over a doorway or in a room was to offer goodwill to visitors. Kissing under the mistletoe was a pledge of friendship. Mistletoe is still forbidden in most Christian churches because of its Pagan associations, but it has continued to have a special place in home and non-religious, public celebrations.
In Iceland, there's a Yule tale about the Jolasveinar, or the Yuletide lads, who begin arriving around December 12th. If you leave your shoe on the windowsill and you've been good, these lads will leave a small toy or piece of fruit for you. If you've been naughty, they will leave you something you will not like at all. Especially bad children, they steal and eat.
As with my other holiday information posts, this is all from research. If you have more or more accurate information, I would love to get ahold of it and post it for others to learn from.