Putting this information together with a book I've read recently called The Master and His Emissary, I would think that the left hemisphere is making the models from sensory input and determining the focus. The book suggests that after creating the response, the right hemisphere updates itself with the new information from the left side. Maybe this means that the right hemisphere does the thinking while the left hemisphere tells us what it is thinking. And 'what it is thinking' is consciousness.

Here's a breakdown of the video as best I can understand it:

PS damaged the right side of her brain
Saw no difference in the two pictures of the houses
Damage to the right-side of her brain left her unaware of everything on her left side
The flames are on the left side of her vision so she doesn’t see them
Nonetheless, her brain processes both fields of her vision
Her brain can see the difference but she didn’t know it
So she would duck from a ball that she didn’t see and wasn’t aware of
So our brain process information that we may not actually experience
Experience of the processing is called consciousness
We are aware of an image in the same way we are aware of ourselves looking at an image
It might be the brain’s imperfect picture of its own activity
The brain processes sensory input and builds models from it
The models are imperfect, just enough for the brain to create responses
Seeing white light is a model because light is really lots of colours
The brain is aware of the configure of our limbs but not extra unnecessary data
The brain needs to make models of its own attention
It needs to be able to focus attention and change it if necessary