The basic answer, of course, is that it has to be a mixture of character traits and personality to make a fully rounded "person" to be the star of your story. So think about where your characters get their traits from and why they have the personality that they do. What would happen to this personality if they were put under stress (especially the ongoing for some time kind of stress)? Would your character still be special or crack under the strain and, if the latter, how can they come back from that? There are stories to be had there!
Also, what is special to your character? What do they consider to be the most important things about themselves and why? Who are their heroes and villains, and why? What possessions do they have that they value the most (and these don't have to be priceless antiques. it could be, say, a battered old teddy bear they've had since very young etc)?