Whether you're talking about a punishment, the weather, or how bad your flu is, severe indicates that it's at the limit of the spectrum.
The austerity of a word like severe serves many purposes. The common usage is to describe tough or painful stuff, like icy snowstorms, merciless punishments, or grim conditions (i.e., a severe depression). If things are severe, they're serious. Severe could also describe a person's haircut if it's brutally short and angular, or their wardrobe if it tends to be all black with no flourishes.
