Prove yourself to who? YOU!! Your self validation is important for your self-esteem. When you have demonstrated your self-worth to your-self; your confidence elevates and you become more valuable to you. 

⁹And the maiden pleased [Hegai] and obtained his favor. And he speedily gave her the things for her purification and her portion of food and the seven chosen maids to be given her from the king’s palace; and he removed her and her maids to the best [apartment] in the harem.

    ¹⁰Esther had not made known her nationality or her kindred, for Mordecai had charged her not to do so.