When you're outraged, you're furious. You might be outraged over the rude treatment you get at a fancy, expensive restaurant.
When something isn't fair, or offends you, it often results in your feeling outraged. You might be outraged on a friend's behalf after her brand new laptop is stolen, or feel outraged about the treatment of inmates at your state's largest prison. The adjective outraged comes from the noun outrage, with its oldest meaning of "evil deed, offense, or crime." The Latin root is ultra, or "beyond."