The city in which Lina lives and works, Ember, is the only place left in the world that has electricity, which means it is the only place that has light. In the aftermath of the huge war and the damage to the Earth and the atmosphere, outside of the controlled space of Ember it is dark all the time. Because of the dark and the potential danger in it, citizens of Ember never leave the confines of their city.
Lina, however, has come to understand that Ember is in danger of extinction if someone doesn't figure out how to repair the generator that is deteriorating, putting out less electricity less reliably as the days go by. Lina and Doon compare discoveries, consider possibilities, and try to find ways to help their city, including their families and friends, survive.
Lina wants to help her city, but she has responsibilities to her grandmother and her little sister as well as her job as a messenger. Leaving Ember would mean going out into the dark, unknown, unprotected world where she would have no information about what to expect or how to protect herself. In spite of all these concerns, that's what she determines to do. "All it would take was the courage to walk away from Ember and into the darkness, and then to keep going."
Lina was very brave in taking the risks she felt were necessary to try to preserve the life of Ember and its citizens.