It means when a person is knocked down on the floor, he can roll right, he can roll left, in order to avoid being hit.
He may also be able to get up instantly and hit a person who is too close. Stuff like that..

Wake up game AKA okizeme means the options for both players when one player is on the floor; the player that has been knocked to the floor and the attacker thats standing up.
The player on the floor has the option to stay on the floor, roll left, roll right, roll back or forward. He may also choose to attack while still on the floor or attack while getting up, or he may just choose to get up like normal.
The attacker has the choice to attack while he is still on the ground, wait for him to get up while staying far away, or let him get up but keep the pressure on him by keeping close to him while he gets up.
Okizeme is is a basic staple in fighting games as it adds alot of straegy and mix up options......and it also could've eliminated most of the infinites in MK:D.

Wake up attacks also include strikes to varying heights = High, Med or Low.
In MKA, the wake up options I've seen are....
1 = Quick roll
2 = Quick attack = As soon as you hit the floor, you stand up while doing an attack. I've seen high and low strikes.
3 = From a high fall, I've seen Kabal skip the fall down animation and just go for a crouching forward kick when he gets to the ground.
As far as I know, you can not stay down in MKA. You have to get up immediately in one of your chosen ways.
Roll
stand up
attack