From Zelda Wiki, the Zelda encyclopedia
Sleeping Zelda is a term used to describe the Princess Zelda that appears in The Adventure of Link. According to a legend passed down within Impa's bloodline, well before the events of The Legend of Zelda, Hyrule was a prosperous land ruled by a king who had two children, an unnamed prince and Princess Zelda. However, an evil magician came to the Prince and told him that the path to true power lay with the Triforce. The prince gives into the wizard's whispers and seeks the Triforce. When the magician tells the prince that his little sister, Zelda, knows the location of the mystical object, the prince demands that Zelda turn the information over to him.
Zelda refuses and, in a rage, the magician puts Zelda into a deep sleep, but dies from the magical backlash. Overcome with grief, the prince seals his sleeping sister in the North Castle and orders that all female descendants of the Hylian monarchy are to be named Zelda. While the princesses before this incident were named Zelda in honor of the original Zelda from Skyward Sword, this marked the beginning of Zelda being named so by law, rather than tradition.
To break the curse a hero must possess the complete Triforce, but obtaining the Triforce of Courage would prove difficult as the king of ages ago had hidden it within the Great Palace. Only one who proved themselves worthy would obtain it. In the end, Link obtained the Triforce of Courage and awoke the sleeping princess from her slumber.