From RWP Wiki
Jiggies (short for "jigsaw pieces") are collectible items in the Banjo-Kazooie series.
Jiggies are the most important items in the series. They are golden jigsaw puzzle pieces with strong magical powers. There are many Jiggies scattered across the worlds in the games. Oddly enough, most non-player characters who come across Jiggies don't actually seem to know what they are (calling them things like "funny-shaped nuggets"). Collecting all the Jiggies is never required to beat Gruntilda, but extra rewards are usually given to players who collect all of them.
In the Games
In Banjo-Kazooie, it is vital to collect Jiggies, as they are needed to fill the magical pictures that open the doors to the levels in Gruntilda's Lair. Whenever one is collected, Banjo and Kazooie do a small dance, then Kazooie eats the Jiggy before game play resumed. There are 10 Jiggies in each of the 9 worlds, plus 10 in the lair, for a grand total of 100, 94 of which are required to access the final battle of the game. If one collects every single Jiggy and fills in every puzzle, there are 2 Jiggies left over in reserve.
In Banjo-Tooie, the purpose remains the same - opening levels - but pulled off differently. Master Jiggywiggy serves as the one who opens levels with the Crystal Jiggy), which he will only do after Banjo and Kazooe collect a certain number of Jiggies and solve an animated jigsaw puzzle. To open the level, one must go to the monolith and solve its puzzle. In this game, there are 10 Jiggies in 8 out of the 9 levels (Cauldron Keep has none), plus 10 in the Isle o' Hags (one of which is gotten from King Jingaling, the rest for saving each of the Jinjo families) for a total of 90, only 70 of which are necessary to access the game's final boss battle.
Banjo-Kazooie: Nuts & Bolts
In Banjo-Kazooie: Nuts & Bolts, Jiggies play a role in opening levels again. In this game, when Jiggies are won in challenge worlds, they are deposited into Jiggy Dispensers in Showdown Town, and can be picked up after exiting the challenge world and returning to Showdown Town. They then must be deposited in a Jiggy Bank, and when a Game Globe is placed on a plinth, doors leading to its respective world will open up. Each door corresponds to a different "act" of the level, and which acts open depends on the Jiggy total. Jiggies are one of many items that are won from challenges, and there are 131 total Jiggies in the game, 75 of which are required to beat the game. 24 of these Jiggies are earned by winning the T.T. Trophies, which are the top prizes in each challenge.
Banjo-Kazooie: Grunty's Revenge
In Banjo-Kazooie: Grunty's Revenge, Jiggies again open levels, although this time Banjo only needs to visit Jiggywiggy with the right amount of Jiggies and touch the Crystal Jiggy, which will open the next level automatically. There are 10 Jiggies in each of the 5 worlds, plus 10 in Spiral Mountain, for a total of 60.
In Banjo-Pilot, Jiggies serve a much different purpose than other games. Bottles has challenges in which you must race him one-on-one while collecting all 6 Jiggies on a track. Collecting every Jiggy while beating Bottles on every track will unlock him as a playable character.