We all use both hemispheres of our brains to some degree but in most people one side dominates.
The concept of right brain and left brain thinking developped from the research in the late 1960s. The human brain has two very different ways of thinking. One (the right brain) is visual and processes information in an intuitive and simultaneous way. The other (the left brain) processes information in an analytical and sequential way.
In general, schools tend to favor left-brain modes of thinkin, while downplaying the right-brain ones. This exercise aims at doping your right brain. Make it everyday in the morning, a few times (until you are told to stop). Benefits should last for 24 hours.