The name Yule or Jól or Jul was already in use well before the year 1000. There is no consensus about the origin of the name. Some say that is originates from the Nordic word for "wheel", others claim that Julius Caesar has lend his name to it, but most likely it is just a name that was given to this specific festival.  Later Christians have transformed the pagan festival into Christmas, celebrating the birth of Christ, a symbol of light. Most of the original mid-winter celebrations and festivities around the world lasted for 12 days or longer. The Christian Advent calendar is probably derived from this, but it starts on December 1st and ends the day before Christmas.

The Yule in Iceland starts on December 12th. Then Stekkjastaur, the first of the Jólasveinar or Yuletide lads, will come down from the mountains into town. Although they were originally seen as playful imps whose main interest seemed to be getting their hands on some of the seasonal food and other goodies, or lurking about trying to do some minor mischief, their role has changed a bit and they have more become "santa's" nowadays. It is an old custom for children to put a shoe in the windowsill, when the Jólasveinar come to town. If the child has behaved good, it will find a little gift in his shoe. If not, there will be a potato in the shoe.
Yule gifts are an old custom too. They have always been of a practical nature. In past centuries a piece of clothing and a pair of ornate shoes (Jólaskór - Yule shoes) was given by the employer. It was not so much a present, but more a reward for work well done. In the early 20th century it became a custom to give a candle to each child and later that was accompanied by.......a deck of cards!
Nowadays toys are a favourite gift and a book is a good second, but there's still always a new piece of clothing too, a necessary ingredient for a good Yule.