The great atmosphere, mysterious story (the game was written by Koizumi who also wrote and directed Majora’s Mask, it’s notable how these two both have a very unique style to them) and characterization in this game has already been adressed, but it’s also of course just excellent in gameplay, level and character/enemy design.
It has great dungeons all around with elaborate and original puzzles, sometimes spanning the entire dungeon. There’s backstories to them, and bosses are intertwined with dungeon themes and stories. The overworld is varied and packed with content and challenge. Certain items can also be used together for extra uses.
It was the first game in the series to do a lot of things that remained in later games; most notably the fishing mini-game and the collectathon and trading side-quests. It was also the first to include unique mini-bosses for each dungeon and a musical instrument that has multiple uses with different songs. The owl was the first guide character, though not yet a constant companion like Navi.
Really it was a wonder it could be on GameBoy at all, as it does pretty much everything better than big brother A Link to the Past on the SNES, except control scheme and graphics but those were obviously a hardware limitation. It’s also almost as big as A Link to the Past, and even had cutscenes!