To me it means, that you believe in yourself, in your abilities, in your knowledge and in control of your insecurities.
Also, self confidence gets built up first within your family, the way we are brought up defines our self confidence in a great deal. Living with an oppressive family can take years to get over.
However, a line should be drawn between self confidence and arrogance; your ability to say with full confidence that you don't know something if you were asked!