The word 'FUSION' comes from the word 'FUSE', which it means to join or to connect together. In DragonBall, it means exactly that, to let two fighters to join together into a single, more powerful and a more dominant fighter.

Potara Fusion.
Potara fusion was created by the dai-kaioshin. He created 2 ear rings that when worn by two different people on opposite ears fuses them together PERMANENTLY. This form of fusion is only ever seen twice in the anime series. The first time it was used was by Kaioushin and Kibito to create Kaiobito. The second time was Vegeta and Goku, they fused to create Veggetto, It was meant to be permanent but Vegetto was then absorbed by Buu canceling out the potara fusion. In any other situation this would have been permanent.

The Fusion Dance
The fusion dance was first tought to Goku after he died the second time against Cell. He later tought this dance to Chibi Trunks and Goten. It was later used in DBGT to create Gogeta, one of the most powerful characters throughout DBZ and DBGT. The fusion dance involves both characters do a funny little dance while shouting out fusion, then touching fingers in the middle. It has to be done perfectly or a 'dud' fusion is created, for example; Veku, a fat gogeta, trunkten, a fat Getenks, or Gotrunks or a skinny Gotenks. The most important thing to remember is that the fusion can only last for 30 minutes, and after that they have to wait for one hour before they can fuse together again. Certain sercainstances can shorten the length of the fusion for example, Being SSJ3 shortens the length of te transformations to 30 mins.

The Namekian Fusion.
The namekian Fusion has only ever been seen twice.
1. Piccolo + Nail = Picconail.
2. Picconail + Kami = Kamicolo.
Although during all these fusions he was still refferred to as Piccolo. This fusion can only be performed between two Nameks, the stronger of the two remains in total control and gains the memories of the fused