The mind is a subject about which very much theorizing, experimenting, and expostulating has occurred in philosophy (studied under the heading philosophy of mind), psychology, and religion (where, in theology, it is often considered alongside such related notions as soul and spirit). Some people think it is synonymous with the brain.
For a computer user the word mind is perhaps best explained as the software of a brain. The mind-body problem can be understood as this software-hardware connection.
So, someone might boldly maintain that we really do not have a mind, or a soul, per se--at least, we do not have any mind or soul that is distinct from our thoughts, perceptions, and other mental events. All there are is a series of thoughts and feelings that are associated with our bodies. There are no minds that are something over and above these thoughts and feelings. This would be the view of someone who held a bundle theory about the mind. The Scottish philosopher David Hume held a theory of mind like this. Buddhism holds a very similar view.
The view of common sense, it seems, is opposed to a bundle theory of the mind. We seem to have a mind, or soul, which is distinct from our thoughts and feelings--and that mind is just exactly what we call our selves. Hume seems to want to deny that there is such a thing as the self. To some people this seems absurd. To them, a substance theory of mind will seem more attractive. On this view, one holds that there is something--one may not know what, but something--which has the thoughts and feelings, and the thoughts and feelings are in our minds, in about the same way that properties inhere in a substance.
Philosophers have not infrequently bandied the phrase "mental substance," and indeed, it has been made central to the ontologies of several philosophers, including most notably Gottfried Leibniz; according to Leibniz, the monad, a "simple soul," is that in terms of which everything else in the universe was to be explained. The notion of mental substance is also basic to the dualism of Rene Descartes. David Hume was very famous for advocating a bundle theory of mind.
However, it should be noted that mind and brain are two quite different concepts -- the first implies an "inside out" look, the second an "outside in" look. We have little more than unprovable assumptions on how exactly the two are related.