Psychologists study the brain and the nervous system because the behavior, perception, cognition we have and do are governed by neurotransmitters that depends on the brain and the nervous system. They understand that the brain is the commander of our whole body therefore controls behavior and mental processes.
To explain things. Everything we see, think, feel, and perceive go through our brain, so knowing about that explains a multitude of things (why people have religion, what causes depression and how to cure it, how to enhance our abilities, etc.).