Anime Appearances
The digivice allows for a connection between the digi-destined and his/her digimon. This enables the digimon to digivolve into the champion stage on it's own. With the help of the Tags and Crests however, they can help the digimon achieve the Ultimate stage.
Below is an explanation of how the digivices were created. (Please note though that there are spoilers within this so read at your own risk)
After the kids witnessed the battle between Parrotmon and Greymon Highten View Terrace a group who is in charge of protecting and defending the Digital World created the digivices. Along with those they also created and maintained the digi eggs for them to hatch for the Digi Destined. But unfortunately the Dark Masters found out about it and destroyed the protectors except for one. That one was Gennai, who hid the Digi Eggs and digivices until another Dark Force made his move.
 Game Appearances
When starting a new game the player gets asked whether he owns a Digivice. The answer has no known effects on the game, besides determining the follow up question. It is also featured in Jijimon's house where it functions as a machine to save the game.
The Digivice is a form of communication tool in the Digital World. You receive calls from your observer and digi-farm usually.
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