A confident person isn't necessarily confident because they are beautiful, powerful, intelligent, popular, or kind. Those traits might help establish their sense of self worth, but in the end, it's about how readily they have accepted themselves (faults and all) and no longer depend so heavily on validation from others.
When illustrating this quote, I imagined it as a piece of advice from an adult to a child. Growing up, we are compelled to depend on others -- parents, teachers, and peers -- to feel accepted and loved. It becomes a habit that is difficult to break. But, if we can learn to know, accept, and love ourselves, then we pave the way for our own freedom. And that freedom in turn allows us to know, accept, and love others as well.