Self-importance is an overblown idea of your own value. Someone who believes they are possibly the most remarkable person in the world has a healthy dose of self-importance.
Self-importance takes a state of being self-confident and exaggerates it wildly. You can imagine why the monarch of a country might have a feeling of self-importance, believing herself to be more worthy than anyone else thanks to her inherited position of power. Anyone with an inflated idea of their value (and a corresponding lack of empathy for others) really needs to tone down their self-importance.