Zelda is one of the key adventure-style rpgs, a forerunner in the fantasy gaming genre. The attraction is in the storyline - advanture and questing.
I'd highly recomend exploring their site where you can check out the individual gaming storylines complete with screenshots.
The basic premise of the original game (released July of '87 for the classic NES) is as follows (taken from the official site:
Ganon, the King of Evil, breaks free from the Dark World and captures Hyrule's beloved Princess Zelda. Before she is caught, Zelda manages to shatter the Triforce of Wisdom and scatter its eight pieces throughout Hyrule. Link swears to recover the Triforce pieces and rescue Princess Zelda from Ganon's clutches.