The Second Quest either refers to the second adventure playable after beating the original The Legend of Zelda or the much-speculated and rumored (although false) prospect of a similar second quest available in Ocarina of Time.
The Legend of Zelda
In the The Legend of Zelda, players could encounter Hyrule on the NES with a new set of puzzles and increased difficulty, allowing for an extended playability.
The select screen for The Legend of Zelda. The image of Link with the sword indicates that it is the Second Quest
Gamers could also enter the first five letters of their name as "ZELDA" in the name input screen to start the second quest automatically.
The Legend of Zelda: Ocarina of Time
In The Ocarina of Time, many players found the then-unprecedented depth of the game to suggest that ideas such as that of a second quest would be far from impossible. Countless discussions, theories and hoaxes about the alleged second quest to obtain the Triforce within the game spread around the internet, although any such endeavor has since been conclusively disproved by Nintendo and skeptical fans. The hype was most likely fueled by the aforementioned sense of depth in the newly-developed OoT environment, nostalgia and internet pranksters. The closest hopefuls might have gotten would have been by bringing unused data left on the game cart during development into play via. a cheat cartridge, or Ura-Zelda-"Another Zelda". This was planned for the 64DD Nintendo 64 add-on, and was finally released in selected copies of the Wind Waker on the Nintendo Gamecube along with the unedited Ocarina of Time. This production was a revamped version of the original quest with excruciatingly difficult new puzzles and challenges, but a seemingly unaltered storyline.