Substance or bundle?
There is a popular problem in philosophy about what the mind is, which can be presented as follows. It is commonplace to wonder what the mind, or soul (if you will), is. One can identify individual thoughts, individual feelings, in one's mind. But what is this mind that has these thoughts and feelings? One can imagine all sorts of mental goings-on, but what is it to imagine the mind itself? It seems the only way we have of understanding, by introspection, what our minds are is by considering various particular thoughts, feelings, decisions, and other events in our minds (i.e., mental events).
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.
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 (though the interpretation of Hume on this point is often one of some controversy) and for arguing forcefully against the idea of mental substance.