The Potara Earrings are exclusively worn by the supreme Gods of the universe, the Kaioshins. When the Elder Kai was introduced to the story it was revealed that these earrings allowed for two beings to permanently fuse into one single, much stronger entity. Supreme Kai and Kibito used this fusion method to become Kibito Kai, and the Saiyans Goku and Vegeta merged into Vegito in an attempt to save their absorbed friends from Majin Buu.
 Potara vs. Fusion Dance
Amongst the Dragonball fan base, there has always been a lot of debates as to which fusion method, and more, specifically, which product they create, is the strongest. Though it can not be said with 100% certainly which is stronger, it is fact that the Potara Earrings are overall better, as this was stated by the Elder Kai. This means that, when looking at the total picture, the Potara product Vegito is better than his Dance counterpart, Gogeta. Mainly because of the Potara's not having a time limit (it is permanent under the normal laws of physics), not requiring the synchronization of power levels prior to fusing, and not having to perform a special pose to fuse.
 History of the Potara Earings
Once Elder kai was out from the Z sword, he explained to Goku, Kabito Kai, and Supreme Kai, how the earrings worked. He let Kabito and Supreme kai fuse into Kabito Kai. It was also explained how Elder Kai was tricked into wearing the earring with an old witch and becoming ugly and old. Then Goku and Vegeta fused to make Vegito.