Tabuu's origins are unknown. What we do know about the character has been explained by series creator, Massahiro Sakurai, on the Smash Bros Dojo. Tabuu is the ruler of the realm of subspace, and made it his goal to merge the outside world with his. However, Tabuu cannot physically leave subspace, so he makes plans to create an army to lead an assault on the outside world as he watches from the depths of Subspace.
The first part of Tabuu's plan was to gain control of the creator of the world, the Master Hand. Using him, Tabuu was able to manipulate Ganondorf, Bowser, and King Deedee to help lead their assault on the world. The second phase was to create Tabuu's soldiers. After discovering the interesting qualities of Mr. Game & Watch's body, he used the material within him, known as Shadow Bugs, to create the Subspace Army. The third step was the take over of the Island of Ancients, which would serve as the Subspace Army's factory for the creation of Subspace Bombs. This lead to the enslavement of the residing R.O.B. robots, and realizing that his kind would be destroyed, the leader of the R.O.Bs agreed to work under Tabuu's control. Out of shame, the leader covered his identity, and became the Ancient Minister. The final step to Tabuu's preparations was the capture of Metaknight's air ship, the Halberd. This ship would be used as the transport between locations for delivering Subspace Bombs to their targets.
The start of Tabuu's assault was the attack on the floating stadium, Terra Firma. Afterwards, Subspace Bombs became launched at various locations in the world, and parts of the world were brought into Subspace.
At a midway point through the story, Meta Knight regains control of the Halberd thanks to Lucario and Snake's assistance, and after the infiltration of the Subspace Bomb factory by Samus and Pikachu, Ganondorf orders all subspace bombs to be detonated. With the factory destroyed, The Subspace Gunship is then used to continue ripping pieces of the world into subspace. It is shortly destroyed by Kirby's Dragoon, and Ganondorf and Bowser are chased back into subspace. Ganondorf then finds it time to usurp his commander, Master Hand, only to find he had been used, as Tabuu reveals himself at this point. With his off-waves, Tabuu transformed everyone into trophies, and used the worlds the bombs had absorbed to create a gigantic maze.
Luckily, King Dedede, Luigi, Ness, and Kirby were revived from their trophy form thanks to Dedede's brooches, and they proceed to revive everyone, friends and enemies, and their common goal is now to find and destroy Tabuu. After traveling through the Great Maze, they arrive at Tabuu's Residence, and as the fiend prepares his off-waves, Sonic arrives on the scene to severely shatter his wings, and a great battle ensues between the fighters and the mysterious ruler of Subspace. Tabuu is eventually defeated, and all the worlds previously taken by subspace are returned to the real world, save for the Island of Ancients, which was completely destroyed by the amount of Subspace Bombs set off.
With this game being his first and only appearance in the Smash Bros series, it does not seem likely for him to return in any sort of form.