Kriss Kringle is most likely the English version of Christkindel or Christkindl, who is the Christ Child and the bearer of gifts for children in many areas of Europe. The Pennsylvania Dutch brought the Christkindl traditions with them when they emigrated to America. Historians speculate that Kriss Kringle came from an English speaking spelling and pronunciation of Christkindl.

Up until the 1500s, Christians throughout Europe associated Saint Nicholas, who was a Bishop of the Catholic Church, with Christmas celebrations. Saint Nicholas visited the children in his Bishop's robes with gifts and treats for good children.
Starting in the 1400s, and gaining popularity throughout the 1500s, the Protestant reformation finally developed into the various Protestant Churches which began to replace the Roman Catholic traditions with traditions of their own.
In many areas in Europe, the Feast of St. Nicholas was abolished and along with it the tradition of Saint Nicholas bringing gifts for children. Saint Nicholas was replaced by the Christ Kindl, which means "Christ Child" by Protestant adherents throughout Europe, notably in Germany and Austria. They urged their following to adopt the Christkindl as their bearer for Christmas and to discard all earlier traditions based on the veneration of the Saints or on earlier non-Christian Yule traditions.

In the 17th century, a Protestant Pastor complained about parents who continued to tell their children that Saint Nicholas had brought them gifts. He admonished them, saying that it is not a good practice because the Christ Child, not Saint Nicholas, gives all good things for body and soul.
In these communities, the messenger of the Christ Child evolved into a beautiful young child or an angel, crowned in gold, bearing a tiny "tree of lights" and gifts from the Baby Jesus.
Various traditions built up over time. In some places, the gifts were brought by the Christkindl, who entered homes through the keyhole of their door on Christmas Eve. In others, the gifts are brought in when the family has gathered around the Christmas tree. A young girl, dressed up in a white robe with golden wings brings the gifts in to the family, playing the part of the Christkindl. Sometimes a young boy will play the part, but it is usually a young girl.
Another tradition is that the Christ Child, Christkindl, comes riding on a gray mule on Christmas Eve. In some traditions, the Christ Child is accompanied by a helper, called Pelznickel, or “Nicholas with fur.” In this tradition Pelznickel visited the children before bedtime, with the Christkindl leaving gifts while the children were asleep. In some communities, adults would dress up in furry outfits and fake beards and play the role of Pelznickel.
In Austria, children write their Christmas wishes on slips of paper and place them on the windowsill for the Christkindl. Morning finds the children checking to see if their slips were taken and hoping that they will receive the gifts wished for.
As traditions throughout Europed melded into modern day Christmas imagery in the Victorian era, penny postcards and illustrations in various publications often showed the Christkindl as a small girl holding a Christmas tree while coming through the forest into a town, often riding a mule, and accompanied by Father Christmas version of Pelznickel.
The little slips of paper with gift requests on them have found their way into modern offices as Kriss Kringle exchanges, where everyone writes their name down on a slip, the slips are all placed in a box or bag, then each person participating in the exchange picks out a slip. The idea is that you buy a small gift for the person on the slip you pick out.