Ah, the Big Key. First, we must first provide some background information. Link, of the Legend of Zelda series, is constantly in search of McGuffins, which he needs in order save Zelda, himself, the world, or any combination of the three. These McGuffins are most often pieces of one of the mystical triforces. However, Link has also quested for musical instruments, crystals, and jewels. The McGuffins aren't just lying about unattended, they're locked away in dungeons and guarded by fierce monsters.
Now, these monsters don't just wander aimlessly. They're under the command of the dungeon's boss. These bosses are all afraid of confrontation because they're guarding a McGuffin, so they've stationed monsters in various rooms to try to kill Link. The bosses have also locked some doors and hidden the keys. After two NES games, the bosses were sick of being easily found, so they locked themselves in rooms that required a Big Key to open. After Link has found enough standard or small keys, he will eventually find the Big Key. Sometimes the Big Key opens multiple doors and/or a big chest, but it always opens the door to the boss's room.
The Big Key is known by three names:
Although the Big Key is best known from the Legend of Zelda series, the concept appears in many games. RPGs are notorious for this. Collect this otherwise meaningless thing so that you can go in there and kick the monster's butt. Some games take a slightly different approach and make the player collect several Big Key-esque items in order to progress through the game. Sly Cooper and the Thievius Raccoonus does this with (yep, you guessed it) keys. Other games featuring Big Keys (or Big Key-like items) include (but are not limited to): the Castlevania series, the Resident Evil series, and the Metroid series (using beams, missiles, and bombs to open doors).
Personally, I think the concept of the Big Key comes from the adventure game. Specifically, I think of the King's Quest series. There were others before it, but King's Quest is the series I'm most familiar with. It taught me that just because you can eat the pie doesn't mean you should. You'll be needing it later; that's why it's in your inventory. It can only be used correctly in one place; just like the Big Key, which is only there to open the door to the boss room.
Source for Big Key names - http://www.gamefaqs.com