Severity is a plain, no-frills hardness––or the degree of hardness. You might talk about the severity of the northern winter, or the severity of your grandfather's discipline.
Severity, with its root in severe, has several nuances. It can mean a hardship, like war’s severity. It also refers to an extreme plainness. Think of the severity of Amish life: no phones, cars, or other modern technology. And you might use it to describe your math teacher’s manner: his severity is indicated by his short, clipped sentences, angry stare, and propensity to fail students without mercy.