A classic theme in the philosophy of mind is the mind-body problem. The mind-body problem boils down to two basic questions. The first question is whether dualism is true or false. Dualism is the theory that there are two basic materials, or kinds of stuff that exist in the world: physical and mental. The two are distinct and cannot be explained solely in terms of the other. For example, a dualist thinks that mental experiences of consciousness cannot be explained solely in terms of physical sciences like biology, chemistry and neuroscience.
The second question is how the mental and physical are related. How does my mind affect my body and how is my body related to my mind? For example, how does it impact my mind when I treat my body poorly? Answers to this question will depend on whether somebody thinks that the mind is a separate kind of stuff or material than the bodily stuff. If you think that what goes on in the mind can be entirely explained in terms of physical material, then there is no problem explaining how the two are connected: the mind is just the brain!
Sven notes that there are epistemological benefits if it turns out that what we call “mental” is really just made up of physical stuff. I can have more knowledge of physical matter than “mental stuff”. I can spatially locate my arm but I cannot spatially locate the location of my experience of pain. Also, I have a different kind of knowledge of physical material than “mental stuff”. My knowledge of physical stuff seems more reliable. One reason for this is that the mental experiences we have are private. Alternatively, physical materials are available for everyone to look at and learn about (in theory). Several people can observe the same physical matter. Only one person can have access to his or her own mental states and mental experiences.