From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Fission (分裂, Bunretsu) is the ability for a single being to split themselves into two different beings. They are more or less equal in terms of power and appearance, but still share a single lifeline.
It is the opposite of Fusion.
When Son Goku first met Kami, he explained to Goku that he and Piccolo Daimao had once been a single being, the Nameless Namekian. The Nameless Namekian had gone to the Heavenly Realm in order to become the apprentice of the then-current Kami of Planet Earth. Kami, however, saw evil within the Nameless Namekian and turned him away. Refusing to give up, the Nameless Namekian dedicated himself to purging the evil within himself. Through Fission, he was successful and split into Kami and Piccolo Daimao, the Nameless Namekian's good and evil counterparts, respectively.
The Nameless Namekian is the only Namekian in the entire series shown to perform Fission, but there are two different and conflicting versions of the event. In Earth's Guardian Emerges, the Nameless Namekian was portrayed as consciously expelling a black ghost-like apparition (presumed to be Piccolo Daimao). In Guru's Gift, when Grand Elder Guru probed Kuririn's mind, Kuririn saw the Nameless Namekian suddenly fall out of his bed and onto the floor. At that point, Piccolo Daimao tore away from the Nameless Namekian's body, thus creating the two beings. One explanation for these conflicting versions is that the original flashback was actually an event from within the Nameless Namekian's subconcious since he appeared to have been sleeping at the start of Guru's vision, which is usually the more well known of the two scenes.
A third version, similar to the first, later appeared in Kami's flashback in "Last Ditch Effort".
Effects and discreprencies
It appears that if either of these two Namekians of Fission gives birth, the offspring can end up mutated and malformed. This is shown when Piccolo Daimao spawned a large number of Mutant Namekians.
When a Namekian split himself into two separate beings, one good and one evil, they still shared a single life. If one should perish of natural or unnatural causes, the other would die within a few seconds. Before Piccolo Daimao died, he inadvertently saved Kami's life by spawning a final son to avenge his death. This new offspring, Piccolo, contained his father's essence (including his techniques and memories) and shared his lifeline with Kami as his father once did. It was not until much later during the fight with the Saiyans when Piccolo was killed that Kami was actually shown dying.
There are some minor discreprencies to the physical appearance of the two new beings in question. Just after Guru's vision, there was a brief shot of Kami and Piccolo Daimao standing side-by-side in their youthful states and looking virtually identical in size and appearance. Earlier on, however, it was shown that Piccolo Daimao dwarfed everyone he met in size, yet Kami seemed to be a much more reasonable size. On the other hand, it was never confirmed at any point that Piccolo Daimao was taller than Kami when they were at the same stage in life. (At one point, Piccolo Daimao wished for restored youth and increased in size thereafter.) Piccolo Daimao in his aged state was portrayed with a much more bulbous head than Kami, though this could actually be attributed to laying eggs. (Piccolo Daimao had already given birth twice in his aged state when first introduced.)
It was shown that when a Namekian split into two, their power decreased a lot since Piccolo Daimao and Kami had such low battle powers separately, but together they could be as powerful as a Super Saiyan as mentioned by Grand Elder Guru. When Piccolo joined with Kami, he was much more powerful than an unmastered Super Saiyan and his battle power was roughly equal to that of Android 17.
After Van Zant and Smitty shot Bee, and later Mister Satan, Fat Boo became more enraged than ever before and used Fission to expel the evil from within his body in order to keep control of his emotions. The evil left Fat Boo in the form of a giant cloud, taking most of his power with him and giving birth to a tall, thin, and gray version of himself named Evil Boo. The good part that was left was named Mister Boo. Evil Boo was the polar opposite of Mister Boo in all aspects apart from apparel (except for him having a dark blue cape where Fat Boo had a purple cape), including the color of his flesh (a drab grey), his incredibly thin body, and gravelly manner of speech.
A battle soon ensued between the two. Evil Boo quickly gained the upper hand and consumed Mister Boo after reflecting Mister Boo's Chocolate Beam. Evil Boo then ate the chocolate Mister Boo and caused a Fusion – this time with the evil dominating – that resulted in Super Boo.
It is named Wakareru (分かれる, Wakareru) in Miracle Battle Carddass Dragon Ball Kai.