This other substance is usually called mind or soul. Materialists, i.e. those who believe that the only substance that exists is matter, argue that all of our cognitive experience can be explained ultimately in terms of electrochemical reactions in the material substrate of the brain.
They reject the notion that we're also possessed of an immaterial mind. For materialists the word "mind" is simply a word we use to describe the function of the brain, just as we use the word "digestion" to describe the function of the stomach.
Perhaps the chief argument that materialists have employed over the years against the notion of an immaterial mind is what's called the "interaction problem". If mind and brain are completely disparate substances, the argument goes, how could they interact? We have no difficulty, for instance, imagining ourselves grasping and lifting a mug with our hand because both our hand and the mug are material objects and we can easily visualize similar substances interacting with each other (parenthetically, it's actually difficult to imagine how even material objects can interact, but more on that below).
However, if we try to imagine how a mind could raise a mug we find that it seems incomprehensible. How does an immaterial mind "grip" a material mug to raise it?
There are various ways to respond to the interaction problem, which philosopher J.P. Moreland calls the most overrated problem in all of philosophy, but physicist William Murray at Uncommon Descent replies by noting that the belief that matter is the fundamental substance that makes up our universe is itself a scientifically obsolete notion.
The problem isn't how mind and matter interact, the problem is why we should think that matter exists objectively at all:
Modern physics has long ago disproved the idea that “matter” exists at all. ...Murray then responds specifically to the interaction problem:
Just because we perceive a world of what we call “matter” doesn’t change the fact that we know no such world actually exists regardless of what our perception tells us. What we call “matter” is a perceptual interpretation of something that is not, in any meaningful sense, “matter”. We know now (current science) that matter is, at its root, entirely “immaterial”, despite what our macro sensory perceptions have told us for millennia (like the sun moving through the sky).
Materialists are clinging to a pre-Victorian perspective of what it is we are perceiving, long since discarded after over a hundred years of experimental results.
Now we get to the so-called “material-immaterial interaction problem”. First, there is no “material world,” so it’s problematic to begin [the discussion] with a term that draws from an archaic, unscientific understanding of what it is we are perceiving.In other words, our inability to explain or imagine how mind and matter interact is no reason to forfeit a belief that they do.
Second, has the “material-material” interaction problem even been addressed, much less “solved”? We have absolutely no idea how “matter” interacts with other “matter”. We can describe the behavior of that interaction, then use a term to refer to that model as if that term was an actual “thing”, but describing the behavior is not explaining the how of the interaction.
When so-called dualism objectors [i.e. materialists] can first explain matter/matter interaction, and when they can tell us what they mean by “material” and “immaterial”, they will then have a meaningful foundation to form a cogent objection to the idea of material/immaterial interaction.
Another way to look at the problem of how fundamentally disparate substances can interact, without denying that there is such a "thing" as matter, is to note that we witness the interaction between material and immaterial all the time. Electrical signals in the material brain produce immaterial sensations like color, sound, and pain. Two magnets will attract each other, but what that magnetic force is and how it pulls another magnet is a mystery. We know these phenomena happen even if we can't explain how they happen.
Likewise with the mind and the interaction problem. Just because we can't explain, or even imagine, how a mind/matter interface would work, we nevertheless have good reason, given our conscious experience, for thinking there is one.
Indeed, belief in the existence of an immaterial mind, long thought to have been buried in the philosophical graveyard, has been recently resurrected as both philosophy and physics breathe new life into it.