Potara are earrings worn by Supreme Kais and attendants of them. They have been worn for many generations now. They are not just used for jewelry though. They hold a second usage that is very powerful. They may be the standard outfit for any Supreme Kai you see. They come in many different colors, so they do not look like anything special. They have no power when worn by one person as a set.
The power is only seen when two people are wearing only one earring on opposite ears. They do not even have to be from the same set. At that point, the two beings are fused together without any warning. This fusion is a permanent. The only way to get out of this fusion is if that person is sucked into a world that does not support the fusion. This is seen when Vegito is absorbed by Super Buu.
Another bad things about this fusion is the inability to power down if you fuse while you are powered up. Going Super Saiyan to fuse can be a great thing, but it would eventually wear down the body and shorten the life. There are good things though as well. When two people merge, their powers are much much stronger than before.
When merging together in a Potara fusion, not only are the two people merged but their clothing as well. The dominant person will show through the voice and facial features. This is shown with Supreme Kai and Kibito. Vegito may have had a double voice and an even look of Veget and Goku since they are both very dominant.
In the Dragon Ball Z series, there are three known Potara merges.
The first was the old witch and old Kai.
The second was Supreme Kai and Kibito.
The third was Goku and Vegeta.