The term Nazi typically refers to someone who affiliates oneself with or is percieved to be affiliated with the ideology of the former National Socialist German Workers Party (Nationalsozialistische Deutsche Arbeiterpartei, commonly called NSDAP or the Nazi Party). The term can be used as a noun or an adjective for such a person or thing.
In pop culture, the term nazi (lowercase "n") can also be coupled with another word to imply overzealousness, aggression or hostility -- negative qualities often associated with the Nazi Party. Such usage was popularized in the November 2, 1995 episode of the successful 1990s sitcom Seinfeld. The plot centered around a soup stand vendor who dispenses his wares in a harsh manner, thus becoming the titular "Soup Nazi." Such usage of the term is often humorous, although it can also be a perjorative. Other examples include feminazi, parking nazi, fashion nazi, and traffic nazi.