Reversals
Known as Reversals in most other Fighting Games, a Wakeup Attack is performed when your character gets up off the ground. If you time a Special Attack the instant you get up, you'll perform a Wakeup Attack. However, not all Special Attacks can be used as a Wakeup Attack. For example, Scorpion can only use the Teleport and Takedown as Wakeup Attacks.
You can actually perform Wakeup Attacks after a Roll Recovery. However, if you perform a Delayed Wakeup, you can no longer trigger Wakeup Attacks.
At this time, there doesn't seem to be any extra benefits to moves performed as Wakeup Attacks. It's just a guarantee that the move comes out the first instant it can.