If you completed the first game (Banjo-Kazooie) 100%, the player was shown a video of the key and eggs, with a promise that they would be used in the sequel. (Banjo-Tooie)
The technology that would have made this possible through what was known as Stop N' Swap. Turn off one of the games, then while the data was still in the RAM of the N64, place the other game in the console. However, Nintendo had made a change to the console that made the time the console clears the RAM post-shutdown to 1 second, making this method impossible. (Tooie had an alternate method to get the items in that game alone, where they did grant bonuses)
In Kazooie, however, in-game cheat codes were discovered that let the player get the items anyways, although they had no function.
The technology that would have made this possible through what was known as Stop N' Swap. Turn off one of the games, then while the data was still in the RAM of the N64, place the other game in the console. However, Nintendo had made a change to the console that made the time the console clears the RAM post-shutdown to 1 second, making this method impossible. (Tooie had an alternate method to get the items in that game alone, where they did grant bonuses)
In Kazooie, however, in-game cheat codes were discovered that let the player get the items anyways, although they had no function.
EDIT: irishcoffee's link below explains it better: http://www.therwp.com/article/dk64-stop-n-swop-connection