The mind is the seat of the self.
The brain is the seat of the mind while the mind inhabits the physical body. The conscious mind arose from the un-conscious, "instinctive mind" of the animals that man deliberately adapted for himself to further his own evolution. Man took the instinctive animal mind further by becoming more conscious, thus the term "standing on the head of the serpent" line from the bible, the serpent representing the unconscious animal mind.
Man needed to direct his new conscious mind with great accuracy to function at a higher level in the physical world than ever before and the instinctive animal mind wasn't cutting it. Man was no longer flowing in his old instinctive nature as the animals did and needed to decide what action to take at any given time. His newly-developed free will gave him the ability to act in any manner necessary no matter how far a field of Universal Love and Truth that would take him in order to experience all the possible variations of a given event in order to expand Universal knowledge. This is what is meant by the phrase: "eating from the tree of knowledge," and knowing "good and evil." This experiment in free will has led us as a species to a stage where we can now see the value and necessity of a world of free will that's in harmony with the Universal Laws of Love and Truth.
Because of the linear nature of time in the physical world our consciousness is very tightly focused in physical reality. It has to be for the sake of survival, that's why one isn't usually going to be aware of other dimensions or entities for example when one is crossing a busy street. Physical survival in our world depends on the mind, nervous system and body focusing on just one situation at a time. This is why activities of the body such as breathing, cell regeneration, and a multitude of other functions usually remain unconscious just as the infinite dimensions and activities of the Higher Self do.
However we're now at a crossroads in evolution once again. There is a new consciousness emerging in the world that's beyond the scope of the mind and much closer to the nature of our true selves similar to the time when Man originally evolved his consciousness from the instinctive animal one. Because of the minds' linear nature it's fixated with imaginary past and future events and focuses large amounts of mental, emotional and physical energy in this direction. It's necessary therefore to go beyond the everyday "normal" focus in order to help facilitate the emergence of this new, higher consciousness. Throughout the ages the great masters realized this and developed ways of transcending the mind's limitations.
By the quieting of your internal mental dialogue you can gradually awaken more and more to this new consciousness. This can be trickier than it sounds if you've never tried it before. Rather than try and force your thoughts to slow down and stop however you only have to observe them as an "outsider" would. Just observe. You also want to be aware of your thoughts as you go about your day as much as possible. Remember that thoughts will eventually condense into a form of some kind or other whether that form is mental, emotional or physical, whether in your body or in worldly circumstances. This mental chatter also uses up a lot of vital energy, using power that could be focused towards what you want to create in life.