These Bakugan do not start off in your unused pile at the beginning of the game; they are off to the side, much like the Reference Cards. When certain requirements are met, such as power level, you swap the Bakugan you are evolving with the Bakugan you are bringing into the game. You then need to skip a turn.
Each Special Evolution Bakugan has their own unique ability that can be used. For example, Splight can move to any other Gate Card on the field after standing. And Quake Dragonoid can be rerolled once per turn. All evolution cards are purple.
Two brawlers are playing a game. Each player has won a Gate Card. It is Player Two's turn. He decides to swap in for Quake Dragonoid. To evolve in that Bakugan, he needs any variation of Dragonoid that has a G-Power of under 650, and the power level needs to be at least two. He decides to swap out his 600 G Pyrus Helix Dragonoid that was in his used pile for his 1000 G Pyrus Quake Dragonoid. The Quake Dragonoid takes the Helix Dragonoid's place in the used pile, and since Player Two must skip a turn after evolving, play continues to Player One.
Most Special Evolution Bakugan in the Anime are commonly used Bakugan, while the Bakugan that they evolve from in the Real Game are one of a kind in the Anime.