Fame

The most important thing about the fame is a recognition. When people say to each other "Hey look at this guy!" or something like "Oh my god, is that...", then you can definetely say that you are famous. Famous people are the ones who achieved something somewhere. Unfortunately for some and fortunately for others fame is not constant. Everyone could be replaced by everyone. Especially in a show business where every year there become more and more new stars. But some persons remain famous even a long time after their death. As an example a classical writers. The famous persons in culture are sometimes called also as a celebrities.
To sum up I'd like to say that the first rule of being famous is working hard for achieving your purpose.