Arrogant is an adjective for describing people who are too proud and look down on others, like supermodels who think their good looks give them a right to do whatever they want.
Arrogant derives from Latin arrogare "to claim," and the idea is that someone is claiming credit or advantages that they are not entitled to. It's close in meaning to haughty and supercilious, but both of those have connotations of coolness and perceived superiority that arrogant does not. An aristocrat could be called all three, but a customs official or traffic cop is more likely to be called arrogant than the other terms.