Self-confidence is, quite obviously, confidence in one's self. This more usually translates, err, transitivly into a belief in one's capabilities. The "I think I can" thing.
I can climb Mt. McKinley, so I have confidence in my mountian climbing abilities.
In order to do something 'different', a highly developed sense of self-confidence is vital. After all, would you ever dare to go against the grain if you didn't believe that you could succeed?