If a business is short-staffed, it has fewer workers than usual. When a small cafe is short-staffed, servers might have to help wash dishes and ring customers up at the cash register.
A short-staffed workplace suffers from an inadequate number of employees. This can be an ongoing problem: "Don't go to that grocery store, they're constantly short-staffed and the lines are always too long." It can also be a temporary situation, like the day several librarians happened to call in sick, leaving the library short-staffed. The term is from the "having too few" sense of short and the verb staff, "provide with workers."