Several thousand years ago, somebody came up with the idea of walls and a roof. For the most part, humanity hasn't looked back. We've also realized that our interaction with artificial spaces is a two-way street.
We can and should design and alter the interiors of our buildings to better suit our needs. If we don't, the environment will negatively affect our energy levels, productivity, mood, and outlook.
One aspect of spatial design is simply practical. If a kitchen is laid out with the fridge in one corner, the sink in another, and the stove in a third, the cook will spend a lot of their time walking back and forth instead of doing something useful. This kind of effect is often much more subtle: in an office building where different departments' personnel are normally isolated from each other, communication will suffer even if nobody is aware of the problem.
The visual impact of a space is also important. Color psychology, for instance, is a real thing: the hues people see while working, socializing, or relaxing have a measurable effect on their feelings. Spatial designers use various techniques to "stage" spaces so that, for example, a doctor's office seems less intimidating or an office layout doesn't distract cubicle dwellers from their work.
Spatial design is a relatively modern field of study. This is because it is really a fusion of interior design, architecture, landscape design, sustainability, visual arts, urban planning, and psychology. You could say that it's the modern, scientifically-backed version of feng shui: organizing spaces so that the "flow" of people, actions, and connections is optimized.
The space being designed may be as small as a room or as large as a town - many of the same principles apply in either case, or anything in between. For this reason, subjects studied in a spatial design course usually include art, lighting design, graphic design, and anthropology with a focus on the use of interior spaces. These "micro-space" subjects are rounded out by courses in surveying, computer-aided design, and geographical information systems; all useful at larger scales. The syllabi of different universities don't all have the same emphasis, so keep your career goals in mind when selecting one.
Successful spatial design students are able to weave all of these threads, plus their knowledge of human sensory experience, into constructive proposals for improving the human and functional aspects of any kind of space. Training at most universities includes plenty of studio work.
Several times during their course of study, students are given a walkthrough of some space and expected to come up with their own innovative mock-up designs for it. Theoretical knowledge and creativity by themselves are not enough. If you want to make a career out of spatial design, you have to be hands-on, solution-orientated, and able to explain why your approach is better than the alternatives.