People may wonder: How is it that Santa Claus can do such things as fly through the air and visit millions of houses and leave billions of presents?
The simplest answer is: "Because he is dead."
A more complex answer is: In late Antiquity and the Middle Ages, it was a common belief that saints were not merely blessed souls in heaven, but were also endowed with the ability to return and walk among the living and perform miracles, or respond to the prayers of the faithful.
+
Although many saints were credited with miracles while they were alive, these are far exceeded by the number attributed to them after their deaths, when, as it seems, they became semi-divine. Indeed, mediæval Christianity may be defined as much by saint-worship as by Christ-worship, and this is still true today in many of the Orthodox and some Catholic churches. With the saints treated as virtual demigods, it was not difficult for every sort of legend to become attached to them.
+
Among these was Nikolaos, the Greek bishop of Myra in Asia Minor, who died in the 4th century. Legends of the wonders he performed during his life began to accrue to him a little over a century after his death; soon these were joined by other miracles said to be performed by him post mortem. After his relics were stolen and shipped to the city of Bari, Italy, his cult spread throughout Catholic Europe.
+
With the Reformation, belief in the miracles of saints was frowned on by Protestant Churches, especially the Calvinist ones that dominated the Netherlands. Nonetheless, it was difficult for popular habits to be changed, and so what had been part of saint-worship became tolerated as a kind of vulgar superstition that was not to be taken seriously. So the miracles of St. Nicholas became the marvels of Sinterklaes, who morphed into "Santa Claus"; still called St. Nick, but without veneration.
@DavidSalo interesting thing about the iconography for the Byzantine Saint Nicholas is that sometimes he's shown with a Bible and a bag of coins rather than an upraised hand. Probably due to the story of his bringing girls out of prostitution by dropping bags of coin through their windows so their fathers could afford a dowry and have them properly married.