Furlough started as a word for time off from military duty. It spread from there to other types of time off, including an employer furloughing (or laying off) employees.
If you're in the military — a pretty tough job — you're probably looking forward to a furlough. That's a leave of absence or bit of time off, kind of like a break or vacation. That kind of a furlough is a great chance for some rest and relaxation. Outside the military, to furlough still means to grant a leave of absence to someone, but often it's a permanent vacation: if your boss furloughed you, he fired you.